Finiteness of cominuscule quantum K-theory

Details Finiteness of cominuscule quantum K-theory Finiteness of cominuscule quantum K-theory

2010-11-30

arxiv.org/abs/1011.6658v1

Mathematics

Algebraic Geometry

19 pages

Scientific paper

The product of two Schubert classes in the quantum K-theory ring of a homogeneous space X = G/P is a formal power series with coefficients in the Grothendieck ring of algebraic vector bundles on X. We show that if X is cominuscule, then this power series has only finitely many non-zero terms. The proof is based on a geometric study of boundary Gromov-Witten varieties in the Kontsevich moduli space, consisting of stable maps to X that take the marked points to general Schubert varieties and whose domains are reducible curves of genus zero. We show that all such varieties have rational singularities, and that boundary Gromov-Witten varieties defined by two Schubert varieties are either empty or unirational. We also prove a relative Kleiman-Bertini theorem for rational singularities, which is of independent interest. A key result is that when X is cominuscule, all boundary Gromov-Witten varieties defined by three single points in X are rationally connected.

Affiliated with

Also associated with

No associations

Rating

Finiteness of cominuscule quantum K-theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Finiteness of cominuscule quantum K-theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finiteness of cominuscule quantum K-theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-573920