Orbifold techniques in degeneration formulas
Dan Abramovich, Barbara Fantechi
TL;DR
This paper introduces an orbifold-based approach to degeneration formulas in Gromov--Witten theory, simplifying the obstruction theory and extending the formulas to orbifold cases.
Contribution
It presents a new orbifold technique for relative and degenerate Gromov--Witten invariants, simplifying the obstruction theory and extending degeneration formulas to orbifolds.
Findings
Simplified the definition of the obstruction theory for Gromov--Witten invariants.
Reproved the degeneration formula using orbifold techniques.
Extended the degeneration formula to orbifold cases.
Abstract
We give an approach for relative and degenerate Gromov--Witten invariants, inspired by that of Jun Li but replacing predeformable maps by transversal maps to a twisted target. The main advantage is a significant simplification in the definition of the obstruction theory. We reprove in our language the degeneration formula, extending it to the orbifold case.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models