Euler characteristics of higher rank double ramification loci in genus one

Abstract

Double ramification loci parametrise marked curves where a weighted sum of the markings is linearly trivial; higher-rank loci are obtained by imposing several such conditions simultaneously. We obtain closed formulae for the orbifold Euler characteristics of double ramification loci, and their higher-rank generalisations, in genus one. The rank-one formula is a polynomial, while the higher-rank formula involves greatest common divisors of matrix minors. The proof is based on a recurrence relation, which allows for induction on the rank and number of markings.

18 pages. Comments welcome. v3: minor changes. Final version to appear in Annali della Scuola Normale Superiore di Pisa - Classe di Scienze