2024/09/15 by Anders Skovsted Buch, Linda Chen, Buch, Anders S. +3
Mathematics · #Commutative Algebra and Its Applications #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology
paper · doi:10.48550/arxiv.2409.09580
A homology class d ∈ H2(X) of a complex flag variety X = G/P is called a line degree if the moduli space M0,0(X,d) of 0-pointed stable maps to X of degree d is also a flag variety G/P'. We prove a quantum equals classical formula stating that any n-pointed (equivariant, K-theoretic, genus zero) Gromov-Witten invariant of line degree on X is equal to a classical intersection number computed on the flag variety G/P'. 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 G/B. Our formulas make it straightforward to compute the big quantum K-theory ring of X modulo degrees larger than line degrees.