The Yamabe invariant of a class of symplectic manifolds

TL;DR

This paper calculates the Yamabe invariant for specific symplectic 4-manifolds obtained via rational blowdown, providing explicit values for a class of minimal symplectic manifolds on the half-Noether line.

Contribution

It introduces a method to compute the Yamabe invariant for symplectic 4-manifolds formed by rational blowdown of Kahler surfaces, expanding understanding of their geometric properties.

Findings

Yamabe invariants are computed explicitly for these manifolds.

Provides examples on the half-Noether line with known Yamabe invariants.

Shows the existence of simply connected minimal symplectic manifolds with determined invariants.

Abstract

We compute the Yamabe invariant for a class of symplectic 4-manifolds of general type obtained by taking the rational blowdown of Kahler surfaces. In particular, for any point on the half-Noether line we exhibit a simply connected minimal symplectic manifold for which we compute the Yamabe invariant.