2022/02/01 by Rosset, Sybille
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2202.00773
Forgetting a subspace from a partial flag yields another partial flag composed of fewer subspaces. This induces a forgetful map π: X → X' between the corresponding flag varieties. We prove here that, for a degree large enough, the variety associated with degree d stable maps sending their marked points within Schubert varieties Xi of X is a rationally connected fibration over its image, which parametrizes degree π_* d stable maps sending their marked points within the Schubert varieties π(Xi) of X'. The Euler characteristic of these varieties are quantum K-invariants. Our result implies equalities between quantum K correlators. We extend these equalities to the equivariant setting. Finally, we study the small quantum K-ring of the universal hyperplane Fl1,n-1. We prove a Chevalley formula in QKs(Fl1,n-1) via geometrical analysis of the space of stale maps to Fl1,n-1 and of its image via evaluation maps.