Work

Counting curves with local tangency constraints

Year: 2021

Type: article

Abstract: We construct invariants for any closed semipositive symplectic manifold which count rational curves satisfying tangency constraints to a local divisor. More generally, we introduce invariants involving multibranched local tangency constraints. We give a formula describing how these invariants arise as point constraints are pushed together in dimension four, and we use this to recursively compute all of these invariants in terms of Gromov–Witten invariants of blowups. As a key tool, we study analogous invariants which count punctured curves with negative ends on a small skinny ellipsoid.

Source: Journal of Topology

DOI: 10.1112/topo.12204

Authors: Dusa McDuff, Kyler Siegel

Institutions: Columbia University, Barnard College, University of Southern California

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: PostDoctoral Research Fellowship