A Note on the existence of stable vector bundles on Enriques surfaces

Abstract

We prove the non-emptiness of $M_{H,Y}(v)$, the moduli space of Gieseker-semistable sheaves on an unnodal Enriques surface $Y$ with Mukai vector $v$ of positive rank with respect to a generic polarization $H$. This completes the chain of progress initiated by H. Kim in \cite{Kim98}. We also show that the stable locus $M_{H,Y}^s(v)\ne \varnothing$ for $v^2>0$. Finally, we prove irreducibility of $M_{H,Y}(v)$ in case $v^2=0$ and $v$ primitive.

18 pages. Comments Welcome!

References in corpus (2)

• Singularities and Kodaira dimension of moduli scheme of stable sheaves on Enriques surfaces
• A note on stable sheaves on Enriques surfaces II

Cited by in corpus (6)

• Projectivity and Birational Geometry of Bridgeland Moduli spaces on an Enriques Surface
• Moduli spaces of stable sheaves on Enriques surfaces
• Some remarks on Bridgeland stability conditions on K3 and Enriques surfaces
• MMP Via Wall-crossing for Moduli Spaces of Stable Sheaves on an Enriques surface
• A note on stable sheaves on Enriques surfaces II
• Descent of tautological sheaves from Hilbert schemes to Enriques manifolds