Wall divisors on irreducible symplectic orbifolds of Nikulin-type

TL;DR

This paper identifies the wall divisors on Nikulin-type irreducible symplectic orbifolds, expanding the understanding of their geometric structure and deformation properties.

Contribution

It determines the wall divisors for a class of orbifolds obtained from K3 surfaces, extending previous work on orbifold singularities and symplectic geometry.

Findings

Wall divisors characterized for Nikulin orbifolds

Extension of wall divisor theory to orbifold singularities

Provides tools for studying deformation equivalence in symplectic orbifolds

Abstract

We determine the wall divisors on irreducible symplectic orbifolds which are deformation equivalent to a special type of examples, called Nikulin orbifolds. The Nikulin orbifolds are obtained as partial resolutions in codimension 2 of a quotient by a symplectic involution of a Hilbert scheme of 2 points on a K3 surface. This builds on the previous article arXiv:2009.04873 in which the theory of wall divisors was generalized to orbifold singularities.