Algebraic Geometry Seminar

---

Shimura Curves Contained in the Jacobian Locus in Small Genus

Speaker: Samuel Grushevsky, Stony Brook University

Location: Warren Weaver Hall 905

Date: Friday, February 28, 2014, noon

Synopsis:

Shimura subvarieties of the moduli space of polarized abelian varieties are defined from some number theoretic data. The locus of Jacobians of curves is a geometrically defined subvariety of the moduli space of principally polarized abelian varieties. Thus the natural question of describing Shimura subvarieites of the Jacobian locus intertwines the questions of number theory and algebraic geometry, and in fact it is expected that in sufficiently high dimension/genus the Jacobian locus contains no Shimura varieties. In contrast, in genus 4 we construct infinitely many Shimura curves contained in the Jacobian locus, and in genus 3 we construct infinitely many Shimura curves contained in the locus of hyperelliptic Jacobians. Based on joint work with Martin Moeller.