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Theta functions, broken lines and 2-marked log Gromov-Witten invariants
1Leibniz University Hannover, Institute of Algebraic Geometry, Welfengarten 1, 30167 Hannover, Germany.
Manuscripta Mathematica
|June 23, 2025
Summary
This study links theta functions to 2-marked log Gromov-Witten invariants for log Calabi-Yau surfaces. This provides an enumerative interpretation for intrinsic mirror constructions and open mirror maps.
Area of Science:
- Algebraic Geometry
- Mathematical Physics
Background:
- Theta functions are defined for varieties with effective anticanonical divisors.
- They have connections to punctured Gromov-Witten invariants.
Purpose of the Study:
- To relate theta functions and their multiplicative structure to 2-marked log Gromov-Witten invariants.
- To extend the correspondence between wall functions and 1-marked log Gromov-Witten invariants.
- To provide an enumerative interpretation for intrinsic mirror constructions.
Main Methods:
- Investigating log Calabi-Yau surfaces with smooth very ample anticanonical divisors.
- Analyzing the multiplicative structure of theta functions.
- Connecting these to 2-marked log Gromov-Witten invariants.
Main Results:
- A relationship is established between theta functions and 2-marked log Gromov-Witten invariants for log Calabi-Yau surfaces.
- This extends known correspondences in log Gromov-Witten theory.
- The findings offer an enumerative interpretation for intrinsic mirror constructions.
Conclusions:
- The study establishes a novel connection between theta functions and higher-marked log Gromov-Witten invariants.
- This work bridges concepts in algebraic geometry and mathematical physics.
- It lays groundwork for understanding open mirror maps and related structures.
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