Logarithmic Gromov–Witten theory with expansions

By Dhruv Ranganathan. Algebraic Geometry, 2019

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We construct a version of relative Gromov-Witten theory with expanded degenerations in the normal crossings setting and establish a degeneration formula for the resulting invariants. Given a simple normal crossings pair $(X,D)$, we construct virtually smooth and proper moduli spaces of curves in $X$ with prescribed boundary conditions along $D$. Each point in such a moduli space parameterizes maps from nodal curves to expanded degenerations of $X$ that are dimensionally transverse to the strata. We use the expanded formalism to reconstruct the virtual class attached to a tropical map in terms of spaces of maps to expansions attached to the vertices.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ac288a0de61e49531602407a2ffa2cc4a8e86e19