Moduli spaces of stable varieties and applications

Project Information

MODSTABVAR

Grant agreement ID: 804334

DOI

10.3030/804334

Project closed

EC signature date 6 September 2019

Start date 1 March 2020

End date 31 August 2025

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 201 370,00

EU contribution

€ 1 201 370,00

Coordinated by

ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
Switzerland

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Peer reviewed articles (12)

Generic vanishing in characteristic p>0 and the geometry of theta divisors

Author(s): Christopher D. Hacon, Zsolt Patakfalvi
Published in: Bollettino dell'Unione Matematica Italiana, Issue vol 15, 2022, Page(s) 215-244, ISSN 1972-6724
Publisher: Unione Matematica Italiana
DOI: 10.1007/s40574-021-00304-6

Weakly special test configurations of log canonical Fano varieties

Author(s): Guodu Chen, Chuyu Zhou
Published in: Algebra & Number Theory, 2022, ISSN 1937-0652
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/ant.2022.16.2415

Gluing theory for slc surfaces and threefolds in positive characteristic

Author(s): Quentin Posva
Published in: Annali della Scuola Normale Superiore di Pisa, 2022, ISSN 0391-173X
Publisher: Stampacchia Guido
DOI: 10.2422/2036-2145.202112_010

On wall crossing for K-stability

Author(s): Chuyu Zhou
Published in: Advances in Mathematics, Issue Volume 413, 2023, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2022.108857

Globally $\pmb{+}$-regular varieties and the minimal model program for threefolds in mixed characteristic

Author(s): Bhargav Bhatt, Linquan Ma, Zsolt Patakfalvi, Karl Schwede, Kevin Tucker, Joe Waldron, Jakub Witaszek
Published in: Publications mathématiques de l'IHÉS, Issue 138, 2023, Page(s) 69-227, ISSN 0073-8301
Publisher: Springer Verlag
DOI: 10.1007/s10240-023-00140-8

Degeneration of log Calabi-Yau pairs via log canonical places

Author(s): Guodu Chen, Chuyu Zhou
Published in: International Mathematics Research Notices, 2022, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnac307

Wall crossing for moduli of stable log pairs

Author(s): Kenneth Ascher, Dori Bejleri, Giovanni Inchiostro, Zsolt Patakfalvi
Published in: Annals of Mathematics, Issue 198, 2023, ISSN 0003-486X
Publisher: Princeton University Press
DOI: 10.4007/annals.2023.198.2.7

Effective semi-ampleness of Hodge line bundles on curves I

Author(s): Chuyu Zhou
Published in: Manuscripta mathematica, 2023, ISSN 0025-2611
Publisher: Springer Verlag
DOI: 10.1007/s00229-023-01465-8

Abundance for slc surfaces over arbitrary fields

Author(s): Quentin Posva
Published in: Épijournal de Géométrie Algébrique, Issue vol 7, 2023, ISSN 2491-6765
Publisher: Épisciences
DOI: 10.46298/epiga.2023.volume7.8803

Product theorem on delta invariants via adding a general boundary

Author(s): Chuyu Zhou
Published in: The Michigan Mathematical Journal, 2022, ISSN 0026-2285
Publisher: University Of Michigan, Department of Mathematics
DOI: 10.1307/mmj/20205993

Ordinary varieties with trivial canonical bundle are not uniruled

Author(s): Zsolt Patakfalvi, Maciej Zdanowicz
Published in: Mathematische Annalen, Issue 380/3-4, 2021, Page(s) 1767-1799, ISSN 0025-5831
Publisher: Springer Verlag
DOI: 10.1007/s00208-021-02165-y

Comparison and Uniruledness of Asymptotic Base Loci

Author(s): Nikolaos Tsakanikas, Zhixin Xie
Published in: to appear in Michigan Mathematical Journal, 2024, ISSN 0026-2285
Publisher: University Of Michigan, Department of Mathematics

Non-peer reviewed articles (13)

On the behavior of stringy motives under Galois quasi-étale covers

Author(s): Javier Carvajal-Rojas, Takehiko Yasuda
Published in: Documenta Mathematica, Issue 30, 2025, Page(s) 709-751, ISSN 1431-0635
Publisher: Deutsche Mathematiker-Vereinigung
DOI: 10.4171/dm/1012

Boundedness of elliptic Calabi–Yau threefolds

Author(s): Stefano Filipazzi, Christopher D. Hacon, Roberto Svaldi
Published in: Journal of the European Mathematical Society, 2024, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jems/1467

Pseudo-effectivity of the relative canonical divisor and uniruledness in positive characteristic

Author(s): Zsolt Patakfalvi
Published in: Épijournal de Géométrie Algébrique, Issue Volume 9, 2025, ISSN 2491-6765
Publisher: Centre pour la Communication Scientifique Directe (CCSD)
DOI: 10.46298/epiga.2025.11595

Index of coregularity zero log Calabi–Yaupairs

Author(s): Stefano Filipazzi, Mirko Mauri, Joaquín Moraga
Published in: Algebra & Number Theory, Issue 19, 2025, Page(s) 383-413, ISSN 1937-0652
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/ant.2025.19.383

Moduli of ℚ-Gorenstein pairs and applications

Author(s): Stefano Filipazzi, Giovanni Inchiostro
Published in: Journal of Algebraic Geometry, Issue 33, 2024, Page(s) 347-399, ISSN 1056-3911
Publisher: American Mathematical Society
DOI: 10.1090/jag/823

On the local étale fundamental group of KLT threefold singularities \n (with an appendix by János Kollár)

Author(s): Javier Carvajal-Rojas, Axel Stäbler
Published in: Algebraic Geometry, 2023, Page(s) 694-728, ISSN 2214-2584
Publisher: Foundation Compositio Mathematics
DOI: 10.14231/ag-2023-025

On K-semistable domains — more examples

Author(s): Chuyu Zhou
Published in: International Journal of Mathematics, Issue 35, 2024, ISSN 0129-167X
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0129167x23501033

Boundedness of log Fano pairs with certain K-stability

Author(s): Konstantin Loginov, Chuyu Zhou
Published in: to appear in International Mathematics Research Notices. IMRN, 2023, ISSN 1073-7928
Publisher: Oxford University Press

On the properness of the moduli space of stable surfaces over Z[1/30]

Author(s): Emelie Arvidsson, Fabio Bernasconi, Zsolt Patakfalvi
Published in: to appear in Moduli, 2024, ISSN 0000-0000
Publisher: Foundation Compositio Mathematica, London Mathematical Society and Cambridge University Press.

On semi-ampleness of the moduli part

Author(s): Stefano Filipazzi, Calum Spicer
Published in: Moduli, Issue 2, 2025, ISSN 2949-7647
Publisher: Wiley
DOI: 10.1112/mod.2025.10004

Log K-stability of GIT-stable divisors on Fano varieties

Author(s): Chuyu Zhou
Published in: Mathematical Research Letters, Issue 31, 2025, Page(s) 1249-1262, ISSN 1073-2780
Publisher: Mathematical Publishing
DOI: 10.4310/mrl.241119010936

Gluing for stable families of surfaces in mixed characteristic

Author(s): Quentin Posva
Published in: Algebraic Geometry, 2025, Page(s) 145-172, ISSN 2214-2584
Publisher: Foundation Compositio Mathematica
DOI: 10.14231/ag-2025-004

Complements and coregularity of Fano varieties

Author(s): Fernando Figueroa, Stefano Filipazzi, Joaquín Moraga, Junyao Peng
Published in: Forum of Mathematics, Sigma, Issue 13, 2025, ISSN 2050-5094
Publisher: Cambridge University Press (CUP)
DOI: 10.1017/fms.2024.69

Other (15)

Perfectoid pure singularities

Author(s): Bhargav Bhatt, Linquan Ma, Zsolt Patakfalvi, Karl Schwede, Kevin Tucker, Joe Waldron, Jakub Witaszek
Published in: 2025
Publisher: arXiv

On the shape of K-semistable domain and wall crossing for K-stability

Author(s): Chuyu Zhou
Published in: 2023
Publisher: arXiv

On Gorenstein Qp-rational threefolds and fourfolds

Author(s): Jefferson Baudin, Zsolt Patakfalvi, Linus Rösler, Maciej Zdanowicz
Published in: 2025
Publisher: arXiv

Chamber decomposition for K-semistable domains and VGIT

Author(s): Chuyu Zhou
Published in: 2023
Publisher: arXiv

Abundance for large Kodaira dimension

Author(s): Chuyu Zhou
Published in: 2021
Publisher: arXiv

On multiplicities of fibers of Fano fibrations

Author(s): Guodu Chen, Chuyu Zhou
Published in: 2022
Publisher: arXiv

On Grauert-Riemenschneider vanishing for Cohen-Macaulay schemes of klt type

Author(s): Jefferson Baudin, Tatsuro Kawakami, Linus Rösler
Published in: 2025
Publisher: arXiv

Effective positivity of Hodge bundles and applications

Author(s): Giulio Codogni, Zsolt Patakfalvi, Luca Tasin
Published in: 2025
Publisher: arXiv

A Counterexample to the Log Canonical Beauville-Bogomolov Decomposition

Author(s): Fabio Bernasconi, Stefano Filipazzi, Zsolt Patakfalvi, Nikolaos Tsakanikas
Published in: 2024
Publisher: arXiv

Birational maps of Severi-Brauer surfaces, with applications to Cremona groups of higher rank

Author(s): Jérémy Blanc, Julia Schneider, Egor Yasinsky
Published in: 2022
Publisher: arXiv

MMP for Enriques Pairs and Singular Enriques Varieties

Author(s): Francesco Antonio Denisi, Ángel David Ríos Ortiz, Nikolaos Tsakanikas, Zhixin Xie
Published in: 2024
Publisher: arXiv

Test ideals in mixed characteristic: a unified theory up to perturbation

Author(s): Bhargav Bhatt, Linquan Ma, Zsolt Patakfalvi, Karl Schwede, Kevin Tucker, Joe Waldron, Jakub Witaszek
Published in: 2024
Publisher: arXiv

The geometry of Frobenius on toric varieties

Author(s): Javier Carvajal-Rojas, Emre Alp Özavcı
Published in: 2025
Publisher: arXiv

Varieties with ample Frobenius-trace kernel

Author(s): Javier Carvajal-Rojas, Zsolt Patakfalvi
Published in: 2021
Publisher: arXiv

The Demailly--Peternell--Schneider conjecture is true in positive characteristic

Author(s): Sho Ejiri, Zsolt Patakfalvi
Published in: 2023
Publisher: arXiv

Book chapters (1)

A Note on Families of K-Semistable Log-Fano Pairs

Author(s): Giulio Codogni, Zsolt Patakfalvi
Published in: Springer Proceedings in Mathematics & Statistics, Birational Geometry, Kähler–Einstein Metrics and Degenerations, 2023, Page(s) 195-203
Publisher: Springer International Publishing
DOI: 10.1007/978-3-031-17859-7_9