Birational geometry of moduli spaces of stable objects on Enriques surfaces

Thorsten Beckmann ^[1]
1. [1] Universitãt Bonn, Alemania
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 1, 2020
Idioma: inglés
DOI: 10.1007/s00029-020-0540-5
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Resumen
- Using wall-crossing for K3 surfaces, we establish birational equivalence of moduli spaces of stable objects on generic Enriques surfaces for different stability conditions. As an application, we prove in the case of a Mukai vector of odd rank that they are birational to Hilbert schemes. The argument makes use of a new Chow-theoretic result, showing that moduli spaces on an Enriques surface give rise to constant cycle subvarieties of the moduli spaces of the covering K3.