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arXiv · 1906.02394

Counting curves with local tangency constraints

Dusa McDuff·Kyler Siegel
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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.

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Dusa McDuff, Kyler Siegel. 2021-09-30. Counting curves with local tangency constraints. https://doi.org/10.1112/topo.12204

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