Symplectic resolutions: deformations and birational maps

TL;DR

This paper studies symplectic resolutions, focusing on their deformations and birational maps, and provides corrected proofs and refined theorems under specific assumptions.

Contribution

It offers a revised analysis of symplectic resolutions, correcting previous errors and establishing new results under restrictive conditions.

Findings

Every symplectic resolution is semismall

Main theorem holds under a technical assumption

Application to G_2 quotient singularities is invalidated

Abstract

Unfortunately, some proofs in the first version of this paper were incorrect. In this revised version, some minor gaps are fixed, one serious mistake found. The main theorem is now claimed only under a restrictive technical assumption. This invalidates the application to quotient singularities by the Weyl group of type $G_2$. Everything else still stands (in particular, the claim that every symplectic resolution is semismall).