Generic vanishing

Events can be found on calendar page, with code GV.

A learning seminar on generic vanishing.

Organizer: Lin Xun

Suggestions of the related topic are welcome. You are also welcome to add references. If you are interested in giving a presentation of one of the topics, please send “number of the topic, name” to the Wechat group or e-mail Lin Xun.

References:

Schnell, lectures on generic vanishing theorem

Hacon, videos of lectures

Time: 02 / 2022 – 06 / 2022, every Wednesday 9:00pm – 11:00pm UTC+8.

Location: Zoom 849 963 1368 Code: YMSC

Talks

Su Weilin

Feb 23

Derived categories and Fourier–Mukai transforms, focus on abelian varieties.

References: Fourier–Mukai transforms in algebraic geometry, D. Huybrechts. Chap 9.

Lin Xun

Mar 02

Hacon’s proof of generic vanishing theorems via Fourier– Mukai transforms for abelian varieties.

References: A derived category approach to generic vanishing, J. Reine Angew. Math. 575 (2004), 173–187.

Su Xiaoyu

Mar 09

Original proof of the generic vanishing theorem. Green, Lazarsfeld.

References: Green, M., Lazarsfeld, R. Deformation theory, generic vanishing theorems, and some conjectures of Enriques, Catanese and Beauville. Invent Math 90, 389–407 (1987).

Wen Xueqing

Mar 16

References: C. Simpson, Subspaces of moduli spaces of rank one local systems, Ann. Sci. ´Ecole Norm. Sup. (4) 26 (1993), 361–401.

Chen Bingyi

Mar 23

The proof using Mixed Hodge modules.

References: M. Popa and C. Schnell, Generic vanishing theory via mixed Hodge modules, Forum Math. Sigma 1 (2013), e1, 60.

Jiang Xiaowei

Mar 30

Birational geometry of varieties of Kodaira dimension zero.

References: J. A. Chen and C. D. Hacon, Characterization of abelian varieties, Invent. Math. 143 (2001), no. 2, 435–447.

Wang Bin

April 6

Inequalities among Hodge numbers of irregular varieties.

References: Popa

Yu Chenglong

April 20

M-regularity on abelian varieties.

References: arXiv:0802.1021

Two times, not decided

Chen-Jiang decomposition. The proofs via Hodge modules and without Hodge modules.

References: J.A. Chen and Z. Jiang, Positivity in varieties of maximal Albanese dimension, J. Reine Angew. Math. 736 (2018), 225–253.

G. Pareschi, M. Popa and C. Schnell, Hodge modules on complex tori and generic vanishing for compact K¨ahler manifolds, Geom. Topol. 21 (2017), no. 4, 2419–2460.

M. B. Villadsen, Chen-Jiang decompositions for projective varieties, without Hodge modules, published online at Math. Z. doi.org/10.1007/s00209-021-02851-2 (2021).

Not decided

More applications on birational geometry.

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