The Euler characteristic of the generalized Kummer scheme of an Abelian threefold

Martin G. Gulbrandsen; Andrea T. Ricolfi

The Euler characteristic of the generalized Kummer scheme of an Abelian threefold

Algebraic Geometry 2017-04-07 v2

Authors: Martin G. Gulbrandsen , Andrea T. Ricolfi

Abstract

Let $X$ be an Abelian threefold. We prove a formula, conjectured by the first author, expressing the Euler characteristic of the generalized Kummer schemes $K^nX$ of $X$ in terms of the number of plane partitions. This computes the Donaldson-Thomas invariant of the moduli stack $[K^nX/X_n]$ .

Keywords

abelian threefold generalized Kummer scheme Euler characteristic plane partition Donaldson-Thomas invariant moduli stack

Cite

@article{arxiv.1506.01229,
  title  = {The Euler characteristic of the generalized Kummer scheme of an Abelian threefold},
  author = {Martin G. Gulbrandsen and Andrea T. Ricolfi},
  journal= {arXiv preprint arXiv:1506.01229},
  year   = {2017}
}

Comments

Corrected the relation with existing literature

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