Relative and orbifold Gromov-Witten invariants

By D. Abramovich, Charles Cadman, Jonathan Wise. 2010

47 citations recorded by the source corpus.

We prove that genus zero Gromov--Witten invariants of a smooth scheme relative to a smooth divisor coincide with genus zero orbifold Gromov--Witten invariants of an appropriate root stack construction along the divisor.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/dc8f989601b120f4f960f9cb68016c602f4b540c

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In Discrete Mathematics and Combinatorics

1. D. Abramovich
2. Steffen Marcus
3. Jonathan Wise
4. Barbara Fantechi
5. Martin Ulirsch
6. Charles Cadman

In Geometry and Topology

1. D. Abramovich
2. Jonathan Wise
3. Qile Chen
4. Steffen Marcus
5. Barbara Fantechi
6. Dhruv Ranganathan
7. Martin Ulirsch
8. Charles Cadman

Citations in the corpus

• Expanded Degenerations and Pairs (2011, methodology): “A central impetus for this article is the need to generalize expansions to twisted expansions, as applied in [2, 3].”
• Comparison theorems for Gromov–Witten invariants of smooth pairs and of degenerations (2012, methodology): “10One reason for considering non-minimal twisting choices is that when r is sufficiently large and divisible, AF g=0(X/V )r is closely related to the moduli space of genus zero orbifold stable maps to a slight modification of X/V (see [ACW10]).”
• Skeletons and Fans of Logarithmic Structures (2015, result): “to aord stacks of maps such as AF (A;D) and Li (A;D). In eect, the virtual birationality of is due to the genuine birationality of A. Similar results were obtained by similar methods in [CMW12] and [ACW10]. SKELETONS AND FANS 31 6.2. Birational invariance for logarithmic stable maps. More general Ar”