Periods of Enriques Manifolds

TL;DR

This paper develops a period domain theory for Enriques manifolds, proving a local Torelli theorem and applying period maps to various geometric constructions involving hyperkaehler manifolds.

Contribution

It introduces period domains for Enriques manifolds, establishes a local Torelli theorem, and applies period maps to moduli spaces and flops, advancing the understanding of their geometry.

Findings

Established a local Torelli theorem for Enriques manifolds.

Constructed period maps for various geometric moduli.

Connected period domains with hyperkaehler geometry.

Abstract

Enriques manifolds are complex spaces whose universal coverings are hyperkaehler manifolds. We introduce period domains for Enriques manifolds, establish a local Torelli theorem, and apply period maps in various situations, involving punctual Hilbert schemes, moduli spaces of stable sheaves, and Mukai flops.