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arXiv · 2103.17050

Rigid ideal sheaves and modular forms

Ádám Gyenge
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Abstract

Let $X$ be a complex smooth quasi-projective surface acted upon by a finite group $G$ such that the quotient $X/G$ has singularities only of ADE type. We obtain an explicit expression for the generating series of the Euler characteristics of the zero-dimensional components in the moduli space of zero-dimensional subschemes on $X$ invariant under the action of $G$. We show that this generating series (up to a suitable rational power of the formal variable) is a holomorphic modular form.

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Ádám Gyenge. 2021-03-31. Rigid ideal sheaves and modular forms. https://arxiv.org/abs/2103.17050

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