TL;DR
This paper reviews Welschinger invariants in real algebraic and symplectic geometry, highlighting their relation to Gromov-Witten invariants and discussing their study via symplectic field theory.
Contribution
It provides an overview of Welschinger invariants, their definitions, and their connections to symplectic field theory, offering insights into their role in real enumerative geometry.
Findings
Welschinger invariants are real analogues of Gromov-Witten invariants.
They can be studied using symplectic field theory techniques.
The paper offers an extended set of notes from a Bourbaki seminar talk.
Abstract
This is an overview of some of the invariants that were discovered by Welschinger in the context of enumerative real algebraic geometry. Their definition finds a natural setup in real symplectic geometry. In particular, they can be studied using techniques from symplectic field theory, of which we also give a sample. Welschinger invariants are real analogues of certain Gromov-Witten invariants. This article is an extended set of notes for a talk at the Bourbaki seminar in April 2011.
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology