On the Euler Characteristic of Generalized Kummer Varieties

1997/11/28 by Olivier Debarre, Debarre, Olivier · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9711035

7 pages, Plain TeX, typeset twice to get references

arxiv created 1997/11/28 · openalex publication_date 1997/11/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We apply the Yau-Zaslow-Beauville method to compute the Euler characteristic of the generalized Kummer varieties attached to a complex abelian surface (a calculation also done by Goettsche and Soergel by different methods). It is related to the number of genus 2 curves on an abelian surface.

Cited by

• Moduli of sheaves and deformation to the normal cone

Related

• The Euler characteristics of generalized Kummer schemes
• Explicit desingularisation of Kummer surfaces in characteristic two via specialisation
• Kummer surfaces and quadratic line complexes in characteristic two
• The automorphism groups of Kummer surfaces in characteristic two and their complex analogues
• Syzygies of Kummer varieties