FRG: Algebraic Geometry and Singularities in Positive and Mixed Characteristic

Summer 2023

We held a Special month at the University of Michigan, May 8th - June 2nd, 2023.

Summer 2022

We held a Learning Workshop and Conference on Algebraic Geometry and Singularities at the University of Washington, June 20 - June 26, 2022.

Summer 2021

We held a Virtual Special Month at the University of Utah, May 17 - June 11th, 2021. Click on the link for more information and to watch the videos.

Published Papers

Arakelov inequalities in higher dimensions, Sándor J Kovács, Behrouz Taji. J. Reine Angew. Math.806(2024), 115-145.

On the 4-dimensional minimal model program for Kahler varieties, Omprokash Das, Christopher Hacon, Mihai Paun. Adv. Math. 443 (2024), Paper No. 109615, 68 pp.

Smooth limits of plane curves of prime degree and Markov numbers, Kristin DeVleming, David Stapleton. J. Éc. polytech. Math.11(2024), 683-731.

Remarks on the existence of minimal models of log canonical generalized pairs, Nikolaos Tsakanikas, Lingyao Xie. Math. Z. 307 (2024), no. 1, Paper No. 20, 39 pp.

Complements, index theorem, and minimal log discrepancies of foliated surface singularities, Jihao Liu, Fanjun Meng, Lingyao Xie. Eur. J. Math.10(2024), no.1, Paper No. 6, 29 pp.

Uniform rational polytopes of foliated threefolds and the global ACC, Jihao Liu, Fanjun Meng, Lingyao Xie. J. Lond. Math. Soc. (2)109(2024), no.6, Paper No. e12950.

Frobenius on the cohomology of thickenings, Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik, Anurag K. Singh, Wenliang Zhang. Int. Math. Res. Not. IMRN(2024), no. 10, 8557-8567.

Existence of flips for generalized lc pairs, Christopher Hacon, Jihao Liu. Cambridge Journal of Mathematics, Volume 11, Number 4, 795-828, 2023

An estimate for F-jumping numbers via the roots of the Bernstein-Sato polynomial, Mircea Mustață. Proc. Amer. Math. Soc.151(2023), no.9, 3751-3761.

Lim Ulrich sequences and Boij-Söderberg cones, Srikanth B. Iyengar, Linquan Ma, Mark E. Walker. Forum Math. Sigma 11(2023), Paper No. e115, 26 pp.

Semi-ampleness of NQC generalized log canonical pairs, Jihao Liu, Lingyao Xie. Adv. Math. 427 (2023), Paper No. 109126, 35 pp.

K-stability for varieties with a big anticanonical class, Chenyang Xu. Épijournal Géom. Algébrique(2023), Art. 7, 9 pp.

The minimal exponent and k-rationality for locally complete intersections, Qianyu Chen, Bradley Dirks, Mircea Mustață. Selecta Math. (N.S.)29(2023), no.4, Paper No. 50, 76 pp.

On a conjecture of Bitoun and Schedler, Mircea Mustață, Sebastian Olano. Int. Math. Res. Not. IMRN(2023), no. 21, 18254-18272.

Values of the F-pure threshold for homogeneous polynomials, Karen E. Smith, Adela Vraciu. J. Lond. Math. Soc. (2) 108 (2023), no. 3, 1004-1035.

The Du Bois complex of a hypersurface and the minimal exponent. Mircea Mustata, Sebastian Olano, Mihnea Popa, Jakub Witaszek. Duke Math. J. 172 (2023), no. 7, 1411-1436.

Prismatic F-crystals and crystalline Galois representations. Bhargav Bhatt, Peter Scholze. Camb. J. Math. 11 (2023), no. 2, 507-562.

Divisors computing minimal log discrepancies on lc surfaces, Jihao Liu, Lingyao Xie. Math. Proc. Cambridge Philos. Soc. 175 (2023), no. 1, 107-128.

Uniform Lech's inequality. Linquan Ma, Ilya Smirnov. Proc. Amer. Math. Soc. 151 (2023), no. 6, 2387-2397.

On the fixed part of pluricanonical systems for surfaces. Jihao Liu, Lingyao Xie. Math. Nachr. 296 (2023), no. 5, 2046-2069.

Lim Ulrich sequences and Lech's conjecture, Linquan Ma, Invent. math. 231, 407-429 (2023).

On the relative minimal model program for fourfolds in positive and mixed characteristic. Christopher Hacon, Jakub Witaszek. Forum Math. Pi 11 (2023), Paper No. e10, 35 pp.

Globally +-regular varieties and the minimal model program for threefolds in mixed characteristic. Bhargav Bhatt, Linquan Ma, Zsolt Patakfalvi, Karl Schwede, Kevin Tucker, Joe Waldron, Jakub Witaszek. Publ. Math. Inst. Hautes Études Sci.138(2023), 69-227.

Finding points on varieties with Macaulay2 Sankhaneel Bisui, Zhan Jiang, Sarasij Maitra, Thai Thanh Nguyen, Karl Schwede. J. Softw. Algebra Geom.13(2023), no.1, 33-43.

Divisors computing minimal log discrepancies on lc surfaces. Jihao Liu, Lingyao Xie. Math. Proc. Cambridge Philos. Soc. 175 (2023), no. 1, 107-128.

Compatible ideals in Q-Gorenstein rings, Thomas Polstra, Karl Schwede. Proc. Amer. Math. Soc.151(2023), no.10, 4099-4112.

FastMinors package for Macaulay2. Boyana Martinova, Marcus Robinson, Karl Schwede, Yuhui Yao. J. Softw. Algebra Geom.13(2023), no.1, 13-31.

Asymptotic Lech's inequality. Craig Huneke, Linquan Ma, Pham Hung Quy, Ilya Smirnov. Adv. Math.372(2020), 107296, 33 pp.

Syntomic complexes and p-adic etale Tate twists. Bhargav Bhatt, Akhil Mathew. Forum Math. Pi 11 (2023), Paper No. e1, 26 pp.

The existence of the Kähler-Ricci soliton degeneration. Harold Blum, Yuchen Liu, Chenyang Xu, Ziquan Zhuang. Forum Math. Pi 11 (2023), Paper No. e9, 28 pp.

Hodge sheaves underlying flat projective families. Sándor Kovács, Behrouz Taji. Math. Z. 303 (2023), no. 3, 75.

Finite generation for valuations computing stability thresholds and applications to K-stability. Yuchen Liu, Chenyang Xu, Ziquan Zhuang. Ann. of Math. (2) 196 (2022), no. 2, 507-566.

Hodge filtration on local cohomology, Du Bois complex, and local cohomological dimension. Mircea Mustata, Mihnea Popa. Forum Math. Pi 10 (2022), Paper No. e22, 58 pp.

Lower bounds on the F-pure threshold and extremal singularities, Zhibek Kadyrsizova, Jennifer Kenkel, Janet Page, Jyoti Singh, Karen E. Smith, Adela Vraciu and Emily E. Witt. Trans. Amer. Math. Soc. Ser. B 9 (2022), 977-1005

The six functors for Zariski-constructible sheaves in rigid geometry. Bhargav Bhatt, David Hansen. Compos. Math. 158 (2022), no. 2, 437-482.

Openness of K-semistability for Fano varieties, Harold Blum, Yuchen Liu, Chenyang Xu. Duke Math. J. 171 (2022), no. 13, 2753-2797.

An analogue of adjoint ideals and PLT singularities in mixed characteristic, Linquan Ma, Karl Schwede, Kevin Tucker, Joe Waldron and Jakub Witaszek. J. Algebraic Geom. 31 (2022), 497-559.

A Buchsbaum theory for tight closure, Linquan Ma and Pham Hung Quy. Trans. Amer. Math. Soc. 375 (2022), 8257-8276.

Multiplicities and Betti numbers in local algebra via lim Ulrich points. Srikanth B. Iyengar, Linquan Ma, Mark E. Walker. Algebra Number Theory 16 (2022), no. 5, 1213-1257.

Generic vanishing in characteristic p>0 and the geometry of theta divisors. Christopher D. Hacon, Zsolt Patakfalvi. Boll. Unione Mat. Ital. 15 (2022), no. 1-2, 215-244.

Boundedness of semistable sheaves. Haoyang Guo, Sanal Shivaprasad, Dylan Spence, Yueqiao Wu. Cambridge University Press, Cambridge, 2022, 126-162.

Algebraic geometry in mixed characteristic. Bhargav Bhatt ICM—International Congress of Mathematicians. Vol. 2. Plenary lectures. 2022 July 6-14. Edited by D. Beliaev and S. Smirnov

Birational automorphism groups and the movable cone theorem for Calabi-Yau complete intersections of products of projective spaces, José Ignacio Yáñez. J. Pure Appl. Algebra 226 (2022), no.10, Paper No. 107093, 22 pp.

F-stable secondary representations and deformation of F-injectivity. Alessandro De Stefani, Linquan Ma. Acta Math. Vietnam. 47 (2022), no. 1, 141-150.

Classification of Frobenius forms in five variables, Zhibek Kadyrsizova, Janet Page, Jyoti Singh, Karen E. Smith, Adela Vraciu and Emily E. Witt. Women in commutative algebra, 353-367, Assoc. Women Math. Ser., 29, Springer, Cham, [2021]

Maximal Cohen-Macaulay complexes and their uses: a partial survey. Srikanth B. Iyengar, Linquan Ma, Karl Schwede, Mark E. Walker, Commutative algebra, 475-500, Springer (2021).

Cubic Surfaces of Characteristic Two. Zhibek Kadyrsizova, Jennifer Kenkel, Janet Page, Jyoti Singh, Karen E. Smith, Adela Vraciu, Emily E. Witt. Trans. Amer. Math. Soc. 374 (2021), no. 9, 6251-6267.

Koszul and local cohomology, and a question of Dutta. Linquan Ma, Anurag K. Singh, Uli Walther. Math. Z. 298 (2021), no. 1-2, 697-711.

On positivity of the CM line bundle on K-moduli spaces. Chenyang Xu, Ziquan Zhuang. Annals of Mathematics. Vol. 192, No. 3, (November 2020), pp. 1005-1068.

Preprints

(2024) F-purity and the F-pure threshold as invariants of linkage, Vaibhav Pandey

(2024) The Briançon-Skoda Theorem via weak functoriality of big Cohen-Macaulay algebras, Sandra Rodríguez-Villalobos, Karl Schwede.

(2024) Boundedness of log Fano cone singularities and discreteness of local volumes Chenyang Xu, Ziquan Zhuang

(2024) On the Canonical Bundle Formula and Adjunction for Generalized Kaehler Pairs, Christopher Hacon, Mihai Paun.

(2024) Minimal model program for algebraically integrable foliations on klt varieties Jihao Liu, Fanjun Meng, Lingyao Xie

(2024) Non-existence of Ulrich modules over Cohen-Macaulay local rings, Srikanth B. Iyengar, Linquan Ma, Mark E. Walker, Ziquan Zhuang.

(2024) Finite generation of split F-regular monoid algebras, Rankeya Datta, Karl Schwede, Kevin Tucker.

(2024) Test ideals in mixed characteristic: a unified theory up to perturbation, Bhargav Bhatt, Linquan Ma, Zsolt Patakfalvi, Karl Schwede, Kevin Tucker, Joe Waldron, Jakub Witaszek

(2023) On the equivalence between the effective adjunction conjectures of Prokhorov-Shokurov and of Li, Jingjun Han, Jihao Liu, Qingyuan Xue.

(2023) h-function, Hilbert-Kunz density function and Frobenius-Poincaré function, Bhargav Bhatt.

(2023) Crystals and Chern classes, Cheng Meng, Alapan Mukhopadhyay.

(2023) Minimal model program for algebraically integrable foliations and generalized pairs, Guodu Chen, Jingjun Han, Jihao Liu, Lingyao Xie.

(2023) Applications of perverse sheaves in commutative algebra. Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik, Anurag K. Singh, Wenliang Zhang.

(2023) On the Minimal Model Program for Kähler 3-folds, Omprokash Das, Christopher Hacon.

(2023) MMP for Generalized Pairs on Kähler 3-folds, Omprokash Das, Christopher Hacon, José Ignacio Yáñez

(2023) Colength, multiplicity, and ideal closure operations II, Linquan Ma, Pham Hung Quy, Ilya Smirnov.

(2023) Vanishing theorems for generalized pairs Bingyi Chen, Jihao Liu, Lingyao Xie

(2023) ACC for generalized log canonical thresholds for complex analytic spaces, Christopher Hacon, Lingyao Xie.

(2023) Vanishing and non-negativity of the first normal Hilbert coefficient, Linquan Ma, Pham Hung Quy.

(2022) Perfectoid signature, perfectoid Hilbert-Kunz multiplicity, and an application to local fundamental groups, Hanlin Cai, Seungsu Lee, Linquan Ma, Karl Schwede, Kevin Tucker.

(2022) Maximal skew sets of lines on a Hermitian surface and a modified Bron-Kerbosch algorithm, Anna Brosowsky, Haoyu Du, Madhav Krishna, Sandra Nair, Janet Page, Tim Ryan.

(2022) Contraction theorem for generalized pairs, Lingyao Xie.

(2022) On Postnikov completeness for replete topoi, Shubhodip Mondal, Emanuel Reinecke.

(2022) Du Bois property of log centers, János Kollár, Sándor J Kovács.

(2022) Ind-étale vs Formally étale, Shubhodip Mondal, Alapan Mukhopadhyay.

(2022) Fano hypersurfaces with no finite order birational automorphisms, Nathan Chen, Lena Ji, David Stapleton.

(2022) V-filtrations and minimal exponents for locally complete intersection singularities, Qianyu Chen, Bradley Dirks, Mircea Mustață, Sebastián Olano.

(2022) Movable cones of complete intersections of multidegree one on products of projective spaces, Michael Hoff, Isabel Stenger, José Ignacio Yáñez.

(2022) Relative Nakayama-Zariski decomposition and minimal models of generalized pairs, Jihao Liu, Lingyao Xie.

(2022) On k-rational and k-Du Bois local complete intersections, Mircea Mustață, Mihnea Popa.

(2022) Stable degenerations of singularities, Chenyang Xu, Ziquan Zhuang.

(2022) Variations of generalised pairs, Caucher Birkar, Christopher D. Hacon.

(2022) The log canonical threshold and rational singularities, Raf Cluckers, János Kollár, Mircea Mustață.

(2022) Absolute prismatic cohomology. Bhargav Bhatt, Jacob Lurie.

(2022) The prismatization of p-adic formal schemes. Bhargav Bhatt, Jacob Lurie.

(2022) Frobenius-Poincare function and Hilbert-Kunz multiplicity, Alapan Mukhopadhyay.

(2022) On generalized lc pairs with b-log abundant nef part. Junpeng Jiao, Jihao Liu, Lingyao Xie.

(2022) Boundedness of polarised Calabi-Yau fibrations. Junpeng Jiao

(2021) Strongly Lech-independent ideals and Lech's conjecture Cheng Meng

(2021) Rational singularities. Sándor Kovács.

(2021) Rational nef and anti-nef polytopes are not uniform, Lingyao Xie.

(2021) Number of singular points on projective surfaces, Jihao Liu, Lingyao Xie.

(2021) On the Boundedness of Canonical Models, Junpeng Jiao.

(2021) Totaro's inequality for classifying spaces. Bhargav Bhatt, Shizhang Li.

(2021) On the termination of the MMP for semi-stable fourfolds in mixed characteristic. Lingyao Xie, Qingyuan Xue.

(2021) On the existence of flips for threefolds in mixed characteristic (0,5). Lingyao Xie, Qingyuan Xue

(2021) Boundedness of elliptic Calabi-Yau threefolds. Stefano Filipazzi, Christopher D. Hacon, Roberto Svaldi.

(2021) Global generation of test ideals in mixed characteristic and applications. Christopher Hacon, Alicia Lamarche, Karl Schwede

(2021) Prismatic cohomology of rigid analytic spaces over de Rham period ring. Haoyang Guo.

(2020) The log minimal model program for Kahler 3-folds. Omprokash Das, Christopher Hacon.

(2020) Excellence, F-singularities, and solidity. Rankeya Datta, Takumi Murayama, Karen E. Smith.

(2020) Effective birationality for sub-pairs with real coefficients. Jingjun Han, Jihao Liu.

(2020) Cohen-Macaulayness of absolute integral closures, Bhargav Bhatt.

Graduate Students

Anna Brosowsky, University of Michigan, student of Karen Smith.

Hanlin Cai, University of Utah, student of Karl Schwede.

Zhiyuan Chen, Princeton University, student of Chenyang Xu.

Haoyang Guo, formerly a student at the University of Michigan, student of Bhargav Bhatt.

Kristine Hampton, University of Washington, student of Sándor Kovács

Kai Huang, MIT, student of Chenyang Xu.

Tafari James, University of Washington, student of Sándor Kovács

Junpeng Jiao, University of Utah, student of Christopher Hacon.

Jihao Liu, formerly a student at the University of Utah, student of Christopher Hacon.

Seungsu Lee, University of Utah, student of Karl Schwede.

Cheng Meng, Purdue University, student of Linquan Ma.

Shubhodip Mondal, University of Michigan, student of Bhargav Bhatt.

Alapan Mukhopadhyay, University of Michigan, student of Karen Smith.

Lu Qi, Princeton University, student of Chenyang Xu.

Sandra Rodríguez-Villalobos, student of Karl Schwede.

Lingyao Xie, University of Utah, student of Christopher Hacon.

Qingyuan Xue, University of Utah, student of Christopher Hacon.

José Ignacio Yáñez, University of Utah, student of Christopher Hacon.

Postdocs

David Stapleton, University of Michigan.

Qianyu Chen, University of Michigan.

Vaibhav Pandey, Purdue University.