Seminar on KSBA Moduli Theory

Upcoming talks:

Families of Varieties of General Type

Reference:

Ja´nos Koll´ar, Families of varieties of general type, 2022.  Chapter 1 ∼ 8.

Schedules:

Lecture 1 (Sep 22, 2022): History of moduli problems.

Lecture 2-3: One-parameter families.

Lecture 4: Families of stable varieties.

Lecture 5-6: Stable pairs over reduced base schemes.

Lecture 7-8: Numerical flatness and stability criteria.

Lecture 9-10: Moduli problems with flat divisorial part.

Lecture 11-12: Cayley flatness.

Lecture 13-14: Moduli of stable pairs.

Projectivity

Lecture 1:  Koll´ar’s ampleness lemma.

Reference: [Kol90].

Lecture 2: Semipositivity theorems for moduli problems.

Reference: [Fuj18].

Lecture 3-5: Projectivity of the moduli space of stable log-varieties.

Reference: [KP17] [PX17].

Explicit Examples

Lecture 1: Plane curves.

Reference: [Hac04].

Lecture 2: Abelian varieties.

Reference: [Ale02]. Speaker:

Lecture 3: K3 surface.

Reference: [Laz16].

Lecture 4: Wall crossing for curves.

Reference: [Has03].

Others: Surfaces in P3, elliptic K3 surfaces, wall crossing in general...

References

[Ale02] Valery Alexeev. Complete moduli in the presence of semiabelian group action.

Ann. of Math. (2), 155(3):611–708, 2002. 2

[Fuj18] Osamu Fujino. Semipositivity theorems for moduli problems. Ann. of Math. (2), 187(3):639–665, 2018. 2

[Hac04] Paul Hacking. Compact moduli of plane curves. Duke Math. J., 124(2):213–257, 2004. 2

[Has03] Brendan Hassett. Moduli spaces of weighted pointed stable curves. Adv. Math., 173(2):316–352, 2003. 2

[Kol90]   J´anos Koll´ar.  Projectivity of complete moduli.  J. Differential Geom., 32(1):235– 268, 1990. 2

[KP17]   S´andor J. Kov´acs 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. 2

[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

[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.