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A Gromov-Witten Theory for Simple Normal-Crossing Pairs Without Log Geometry
Hsian-Hua Tseng1, Fenglong You2
1Department of Mathematics, Ohio State University, 100 Math Tower, 231 West 18th Ave., Columbus, OH 43210 USA.
Communications in Mathematical Physics
|June 26, 2023
Summary
This study introduces a new Gromov-Witten theory for simple normal crossing divisors, proving key properties like relative quantum cohomology and Virasoro constraints. This framework offers an alternative mirror construction and confirms a Frobenius structure conjecture.
Area of Science:
- Algebraic Geometry
- Mathematical Physics
- String Theory
Background:
- Gromov-Witten theory is a powerful tool in algebraic geometry and theoretical physics.
- Understanding theories relative to divisors is crucial for advanced mathematical constructions.
Purpose of the Study:
- To define and explore a new Gromov-Witten theory relative to simple normal crossing divisors.
- To establish structural properties and connections to existing theories.
Main Methods:
- The study defines a new theory as a limit of Gromov-Witten theory of multi-root stacks.
- It proves properties including relative quantum cohomology and Virasoro constraints (genus zero).
Main Results:
- A novel Gromov-Witten theory relative to simple normal crossing divisors is established.
- Key structural properties, including relative quantum cohomology and Virasoro constraints, are proven.
- The theory provides an alternative mirror construction and confirms a Frobenius structure conjecture.
Conclusions:
- The developed theory offers a new perspective on Gromov-Witten theory and its applications.
- It provides a unified framework for studying mirror symmetry and related conjectures.
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