A finiteness theorem on symplectic singularities

TL;DR

This paper proves that for fixed positive integers N and d, there are only finitely many conical symplectic varieties of dimension 2d with maximal weights N, up to isomorphism, establishing a finiteness property in symplectic geometry.

Contribution

The paper establishes a finiteness theorem for conical symplectic varieties with fixed dimension and maximal weight, a new result in the classification of symplectic singularities.

Findings

Finite number of conical symplectic varieties for fixed N and d

Finiteness up to isomorphism

Maximal weight bounds the classification

Abstract

For positive integers N and d, there are only finite number of conical symplectic varieties of dimension 2d with maximal weights N, up to isomorphism. The maximal weight of a conical symplectic variety X is, by definition, the maximal weight of the minimal homogeneous generators of the coordinate ring R of X.