Orbifold techniques in degeneration formulas

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.

Some material which is now in arXiv:1406.2166 and in arXiv:1110.2976 was removed

References in corpus (4)

• Relative orbifold Gromov-Witten theory and degeneration formula
• Logarithmic Stable Maps
• Comparison theorems for Gromov-Witten invariants of smooth pairs and of degenerations
• A Generalization of Fulton-MacPherson Configuration Spaces

Cited by in corpus (24)

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• Relative orbifold Gromov-Witten theory and degeneration formula
• The degeneration formula for stable log maps
• Invariance of quantum rings under ordinary flops: III
• Comparison theorems for Gromov-Witten invariants of smooth pairs and of degenerations
• The local-orbifold correspondence for simple normal crossings pairs
• The degeneration formula for logarithmic expanded degenerations
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• The SYZ mirror symmetry and the BKMP remodeling conjecture
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• Expanded degenerations and pairs
• Splitting of Gromov-Witten Invariants with Toric Gluing Strata
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• A Formula of the One-leg Orbifold Gromov-Witten Vertex and Gromov-Witten Invariants of the Local $\cB\bZ_m$ Gerbe
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• A survey on mixed spin P-fields
• Orbifold Gromov-Witten Invariants of Weighted Blow-up at Smooth Points
• On orbifold Gromov-Witten theory in codimension one