Work

K-theoretic Gromov–Witten invariants of line degrees on flag varieties

Year: 2024

Type: article

Abstract: A homology class [Formula: see text] of a complex flag variety [Formula: see text] is called a line degree if the moduli space [Formula: see text] of 0-pointed stable maps to X of degree d is also a flag variety [Formula: see text]. We prove a quantum equals classical formula stating that any n-pointed (equivariant, [Formula: see text]-theoretic, genus zero) Gromov–Witten invariant of line degree on X is equal to a classical intersection number computed on the flag variety [Formula: see text]. We also prove an n-pointed analogue of the Peterson comparison formula stating that these invariants coincide with Gromov–Witten invariants of the variety of complete flags [Formula: see text]. Our formulas make it straightforward to compute the big quantum [Formula: see text]-theory ring [Formula: see text] modulo the ideal [Formula: see text] generated by degrees d larger than line degrees.

Source: International Journal of Modern Physics A

DOI: 10.1142/s0217751x24460138

Authors: Anders S. Buch, Linda Chen, Weihong Xu

Institutions: Rutgers, The State University of New Jersey, Swarthmore College, California Institute of Technology

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

OpenAlex ID: W4402284716

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Cites: 21

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Related to: 10