Welschinger invariants of Blow-ups of symplectic 4-manifolds

TL;DR

This paper investigates how Welschinger invariants of symplectic 4-manifolds change under blow-up operations and point configuration variations, providing new formulae and reproofs of existing wall crossing results.

Contribution

It introduces blow-up formulae for Welschinger invariants and analyzes their behavior under point configuration changes, including a reproof of Welschinger's wall crossing formula.

Findings

Derived blow-up formulae for Welschinger invariants.

Analyzed the variation of invariants with point configuration changes.

Reproved Welschinger's wall crossing formula.

Abstract

Using the degeneration technique, one studies the behavior of Welschinger invariants under the blow-up, and obtains some blow-up formulae of Welschinger invariants. One also analyses the variation of Welschinger invariants when replacing a pair of real points in the real configuration by a pair of conjugated points, and reproves Welschinger's wall crossing formula.