Distinguishing symplectic blowups of the complex projective plane

TL;DR

This paper characterizes when symplectic manifolds obtained from the complex projective plane via blowups are symplectomorphic, based on their defining parameters.

Contribution

It provides a complete classification of symplectic blowups of the complex projective plane up to symplectomorphism.

Findings

Identifies parameter conditions for symplectomorphism

Classifies symplectic blowups by size parameters

Provides explicit criteria for equivalence

Abstract

A symplectic manifold that is obtained from the complex projective plane by k blowups is encoded by k+1 parameters: the size of the initial complex projective plane, and the sizes of the blowups. We determine which values of these parameters yield symplectomorphic manifolds.