Spring 2023 A: Birational Geometry Preprint Seminar

Time: Monday, 18:30-19:50
Location: Ningzhai W11

Description

This is a weekly reading seminar on recent (<2 years old) preprints in birational geometry. Each week, a speaker will choose any paper he or she likes to present.

Speakers are suggested to limit their talks to 60 minutes, leaving the remaining time free for other participants to discuss potential applications and further developments.

Tentative Schedule

	Date	Speaker	Topic	References
Week 1	Feb 20, 2023	No seminar
Week 2	Feb 27, 2023	No seminar
Week 3	Mar 6, 2023	Junpeng Jiao	Junpeng Jiao, Locally stable degenerations of log Calabi-Yau pairs	arXiv:2302.08352
Week 4	Mar 13, 2023	Xiaowei Jiang	Ziquan Zhuang, On boundedness of singularities and minimal log discrepancies of Kollár components II	arXiv:2302.03841
Week 5	Mar 20, 2023	Bingyi Chen	Bingyi Chen, Explicit bound for singularities on the base of a Fano type fibration of relative dimension one	arXiv:2210.08469
Week 6	Mar 27, 2023	No seminar
Week 7	Apr 3, 2023	Fei Si (PKU)	Long Pan, Fei Si, Haoyu Wu, K moduli of log del Pezzo pairs	arXiv:2303.05651
Week 8	Apr 10, 2023	No seminar	Moduli Spaces in Mathematics Workshop & Conference
Week 9	Apr 17, 2023	Yu Zou	Minzhe Zhu, On explicit birational geometry for weak Fano varieties and polarised Calabi-Yau varieties	arXiv:2301.07462, arXiv:2303.12292
Week 10	Apr 24, 2023	No seminar	2023 Workshop on Explicit Birational Geometry
Week 11	Mar 1, 2023	No seminar	International Workers' Day
Week 12	May 8, 2023	No seminar	Conference on Algebraic Geometry and Related Topics
Week 13	May 15, 2023	No seminar
Week 14	May 22, 2023	Yu Zou	Chen Jiang, Yu Zou, An effective upper bound for anti-canonical volumes of singular Fano threefolds	arXiv:2304.06347
Week 15	May 29, 2023	No seminar
Week 16	Jun 5, 2023	No seminar

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Spring 2023 B: KSBA Moduli Theory II

Time: Monday, 20:00-21:30
Location: Ningzhai W11

References

• [Kol90] János Kollár. Projectivity of complete moduli. J. Differential Geom., 32(1):235–268, 1990.
• [Fuj18] Osamu Fujino. Semipositivity theorems for moduli problems. Ann. of Math. (2), 187(3):639–665, 2018.
• [Fuj20] Osamu Fujino. Vanishing and semipositivity theorems for semi-log canonical pairs. Publ. Res. Inst. Math. Sci. 56 (2020), no. 1, 15–32.
• [KP17] Sándor J. Kovács and Zsolt Patakfalvi. Projectivity of the moduli space of stable log-varieties and subadditivity of log-Kodaira dimension. J. Amer. Math. Soc., 30(4):959–1021, 2017.
• [PX17] Zsolt Patakfalvi and Chenyang Xu. Ampleness of the CM line bundle on the moduli space of canonically polarized varieties. Algebr. Geom., 4(1):29–39, 2017.
• [Ale02] Valery Alexeev. Complete moduli in the presence of semiabelian group action. Ann. of Math. (2), 155(3):611–708, 2002. 2
• [Has03] Brendan Hassett. Moduli spaces of weighted pointed stable curves. Adv. Math., 173(2):316–352, 2003.
• [Hac04] Paul Hacking. Compact moduli of plane curves. Duke Math. J., 124(2):213–257, 2004.
• [Laz16] Radu Laza. The KSBA compactification for the moduli space of degree two K3 pairs. J. Eur. Math. Soc. (JEMS), 18(2):225–279, 2016. 2
• [ABIP21] Kenneth Ascher, Dori Bejleri, Giovanni Inchiostro, Zsolt Patakfalvi. Wall crossing for moduli of stable log pairs. Annals of Mathematics, To appear. arXiv:2108.07402.

Tentative Schedule

	Date	Speaker	Topic	References
Week 1	Feb 20, 2023	No seminar
Week 2	Feb 27, 2023	No seminar
Week 3	Mar 6, 2023	Xiaowei Jiang	Semipositivity theorems for moduli problems	[Fuj18][Fuj20]
Week 4	Mar 13, 2023	Fei Si (PKU)	Kollár's ampleness lemma	[Kol90, §2-3]
Week 5	Mar 20, 2023	No seminar
Week 6	Mar 27, 2023	No seminar
Week 7	Apr 3, 2023	No seminar
Week 8	Apr 10, 2023	Ruitong Zhang	Ampleness of the CM line bundle	[PX17]
Week 9	Apr 17, 2023	No seminar
Week 10	Apr 24, 2023	No seminar	2023 Workshop on Explicit Birational Geometry
Week 11	Mar 1, 2023	No seminar	International Workers' Day
Week 12	May 8, 2023	No seminar	Conference on Algebraic Geometry and Related Topics
Week 13	May 15, 2023	No seminar
Week 14	May 22, 2023	No seminar
Week 15	May 29, 2023	No seminar
Week 16	Jun 5, 2023	Bingyi Chen	Wall crossing for moduli of stable log pairs	[ABIP21]

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Fall 2022 B: Moduli of Stable Minimal Models

Time: Thursday, 10:00-12:00
Location: Online

References

• [Bir22] Caucher Birkar, Moduli of algebraic varieties, arXiv:2211.11237.

Schedule

	Date	Speaker	Topic	References
Lecture 1	Dec 1, 2022	Caucher Birkar	Introduction	[Bir22,§1]
Lecture 2	Dec 8, 2022	Bingyi Chen	Stein degree on log Calabi-Yau fibrations	[Bir22,§3]
Lecture 3	Dec 22, 2022	Xiaowei Jiang	Lc stable minimal models	[Bir22,§4]
Lecture 4	Dec 29, 2022	Yu Zou	Slc stable minimal models	[Bir22,§5-6]
Lecture 5	Jan 5, 2023	Ruitong Zhang	Good minimal models in families	[Bir22,§7-8]
Lecture 6	Jan 12, 2023	Junpeng Jiao	Coarse moduli spaces of stable minimal models	[Bir22,§9-10]
Lecture 7	Jan 19, 2023	Caucher Birkar	Examples of moduli spaces and some questions	[Bir22,§11]

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Fall 2022 A: KSBA Moduli Theory

Time: Thursday, 18:30-20:30
Location: Jinchunyuan West Building, 2nd Floor

References

• [Kol23] János Kollár, Families of varieties of general type (to appear), Cambridge Tracts in Mathematics 231, 2023. Book link.

Schedule

	Date	Speaker	Topic	References
Lecture 1	Sep 22, 2022	Fuxin Xu	History of moduli problems	[Kol23,§1]
Lecture 2-3	Sep 29, 2022	Qiwei Zhu	One-parameter families	[Kol23,§2]
Lecture 4	Oct 13, 2022	Junpeng Jiao	Families of stable varieties	[Kol23,§3]
Lecture 5-6	Oct 27, 2022	Yu Zou	Stable pairs over reduced base schemes	[Kol23,§4]
Lecture 7	Nov 10, 2022	Bingyi Chen	Numerical flatness and stability criteria	[Kol23,§5]
Lecture 8	Nov 17, 2022	Xiaowei Jiang	Moduli problems with flat divisorial part	[Kol23,§6]
Lecture 9	Nov 24, 2022	Bingyi Chen	Moduli of stable pairs	[Kol23,§8]

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Spring 2022: Iikata Conjecture

Time: Monday, 19:00-21:00
Location: Jingzhai 304

References

• [Fuj20] Osamu Fujino, Iitaka conjecture—an introduction, SpringerBriefs in Mathematics. Springer, Singapore, 2020.

Schedule

	Date	Speaker	Topic	References
Lecture 1	2022-4-4	Bingyi Chen	Good minimal models of klt pairs over abelian varieties	[BC15]
Lecture 2	2022-4-11	Bingyi Chen	Good minimal models of lc pairs over abelian varieties	[Hu18']
Lecture 3	2022-4-18	Xiaowei Jiang	An introduction to Iitaka conjecture	[Fuj20, §1-3]
Lecture 4	2022-4-25	Xiaowei Jiang	Iitaka conjecture for varieties fibred over abelian varieties	[HPS18]
Lecture 5	2022-5-2	Qiwei Zhu	Iitaka conjecture for varieties fibred over varieties of general type	[Fuj20, §4.1-4.2]
Lecture 6	2022-5-9	Qiwei Zhu	Iitaka conjecture for fibre space whose generic Fiber is of general type	[Fuj20, §4.3]

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Fall 2021: Minimal Model Program

Time: Monday, 19:00-21:00
Location: Jinchunyuan West Building, 2nd Floor

References

• [KM98] János Kollár and Shigefumi Mori, Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics 134, 1998.

Schedule

	Speaker	Topic	References
Lecture 1	Xiaowei Jiang	Overview of the Minimal Model Program
Lecture 2-3	Qiwei Zhu	Cone of curves and positivity	[KM98, §1.3&1.5]
Lecture 4-5	Bingyi Chen	Base point free theorem and the cone theorem	[KM98, §3.1-3.3]
Lecture 6	Xun lin	Brational geometry and derived category	[Kaw17']
Lecture 7	Xiaowei Jiang	Existence of minimal models for varieties of log general type	[BCHM10]
Lecture 8	Xiaowei Jiang	Abundance for varieties of numerical dimension zero	[Gon13]
Lecture 9	Xiaowei Jiang	Rational connectedness of Fano type varieties	[HM07]
Lecture 10	Bingyi Chen	An introduction to generalised pairs	[Bir21]
Lecture 11	Qiwei Zhu	Weak Zariski decompositions and log terminal models	[HL22]

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