Schedule:

11/03: Introduction and basics

Speaker: Jian Xiao

Reference: [1], [2]

11/10: EKL’s effective lower bound I

Speaker: Shijie Shang

Reference: [2], [3]

11/17: EKL’s effective lower bound II

Speaker: Shijie Shang

Reference: [2], [3]

11/24: Lower bound via Newton-Okounkov bodies I

Speaker: Jiajun Hu

Reference: [4], [5], [6]

12/01: Lower bound via Newton-Okounkov bodies II

Speaker: Jiajun Hu

Reference: [4], [5], [6]

12/08: Canonical growth condition I

Speaker: Xing Lu

Reference: [7]

12/15: Canonical growth condition II

Speaker: Xing Lu

Reference: [7]

12/22: Relation with K-stability I

Speaker: Junyu Cao

Reference: [8]

12/29: Relation with K-stability II

Speaker: Junyu Cao

Reference: [8]

01/05: Relation with diophantine approximation and Roth’s theorem

Speaker: TBD

Reference: [9]

01/12: Construction for cycles and vector bundles

Speaker: Jian Xiao

Reference: [10], [11]

References:

[1] J.-P. Demailly. Singular Hermitian metrics on positive line bundles, in: Complex Algebraic Varieties, Bayreuth, 1990, in: Lecture Notes in Math., vol. 1507, Springer, Berlin, 1992, pp. 87–104.

[2] R. Lazarsfeld. Positivity in Algebraic Geometry. Classical Setting: Line Bundles and Linear Series, Ergeb. Math. Grenzgeb. (3), vol. 48, Springer-Verlag, Berlin, 2004.

[3] L. Ein, O. Küchle, R. Lazarsfeld. Local positivity of ample line bundles, J. Differ. Geom. 42 (2) (1995) 193–219.

[4] A. Ito. Okounkov bodies and Seshadri constants, Adv. Math. 241 (2013) 246–262.

[5] D. Witt Nyström. Okounkov bodies and the Kähler geometry of projective manifolds, arXiv:1510.00510.

[6] K. Kaveh. Toric degenerations and symplectic geometry of smooth projective varieties, J. Lond. Math. Soc. (2) 99 (2019), no. 2, 377–402.

[7] D. Witt Nyström. Canonical growth conditions associated to ample line bundles, Duke Math. J. 167 (2018), no. 3, 449–495.

[8] Z. Zhuang, H. Abban. Seshadri constants and K-stability of Fano manifolds, to appear in Duke Math. J.

[9] D. McKinnon, M. Roth. Seshadri constants, diophantine approximation, and Roth’s theorem for arbitrary varieties, Invent. Math. 200 (2015), no. 2, 513–583.

[10] M. Fulger, T. Murayama. Seshadri constants for vector bundles, J. Pure Appl. Algebra 225 (2021), no. 4, Paper No. 106559, 35 pp.

[11] N. McCleerey, J. Xiao. Polar transform and local positivity for curves, Ann. Fac. Sci. Toulouse Math. (6) 29 (2020), no. 2, 247–269.