MMP via wall-crossing for moduli spaces of stable sheaves on an Enriques surface

Howard Nuer, Kōta Yoshioka

Research output: Contribution to journalArticlepeer-review

Abstract

We use wall-crossing in the Bridgeland stability manifold to systematically study the birational geometry of the moduli space Mσ(v) of σ-semistable objects of class v for a generic stability condition σ on an arbitrary Enriques surface X. In particular, we show that for any other generic stability condition τ, the two moduli spaces Mτ(v) and Mσ(v) are birational. As a consequence, we show that for primitive v of odd rank Mσ(v) is birational to a Hilbert scheme of points. Similarly, in even rank we show that Mσ(v) is birational to a moduli space of torsion sheaves supported on a hyperelliptic curve when ℓ(v)=1. As an added bonus of our work, we prove that the Donaldson-Mukai map θv,σ:v→Pic(Mσ(v)) is an isomorphism for these classes. Finally, we use our classification to fully describe the geometry of the only two examples of moduli of stable sheaves on X that are uniruled (and thus not K-trivial).

Original languageEnglish
Article number107283
JournalAdvances in Mathematics
Volume372
DOIs
StatePublished - 7 Oct 2020
Externally publishedYes

Keywords

  • Bridgeland stability
  • Enriques surfaces
  • Moduli of sheaves

ASJC Scopus subject areas

  • General Mathematics

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