Effective divisors on moduli spaces of curves and abelian varieties. (English) Zbl 1317.14060

Chen, Dawei; Farkas, Gavril; Morrison, Ian

Hassett, Brendan (ed.) et al., A celebration of algebraic geometry. A conference in honor of Joe Harris’ 60th birthday, Harvard University, Cambridge, MA, USA, August 25–28, 2011. Providence, RI: American Mathematical Society (AMS); Cambridge, MA: Clay Mathematics Institute (ISBN 978-0-8218-8983-1/pbk). Clay Mathematics Proceedings 18, 131-169 (2013).

Authors’ abstract of the arXiv version: This paper is an expository survey of results about the effective divisors on moduli spaces, with a focus on what is known about the effective cones of moduli spaces of stable curves and of principally polarized abelian varieties. This version incorporates clarifications and suggestions of Ana-Maria Castravet and the referee, both of whom we thank.
For the entire collection see [Zbl 1275.14003].

MSC:

14H10	Families, moduli of curves (algebraic)
14H51	Special divisors on curves (gonality, Brill-Noether theory)
14D22	Fine and coarse moduli spaces
14E30	Minimal model program (Mori theory, extremal rays)

Keywords:

effective divisors; moduli spaces; principally polarized abelian varieties