Rigid ideal shaves and modular forms

Gyenge, Ádám (2022) Rigid ideal shaves and modular forms. QUARTERLY JOURNAL OF MATHEMATICS, 73 (3). pp. 1035-1053. ISSN 0033-5606

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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 of 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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