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arXiv · 2502.12281

Euler characteristics of higher rank double ramification loci in genus one

Luca Battistella·Navid Nabijou
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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.

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Luca Battistella, Navid Nabijou. 2025-02-17. Euler characteristics of higher rank double ramification loci in genus one. https://arxiv.org/abs/2502.12281

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