Asian Journal of Mathematics
Volume 20 (2016)
Rational connectedness implies finiteness of quantum $K$-theory
Pages: 117 – 122
Let $X$ be any generalized flag variety with Picard group of rank one. Given a degree $d$, consider the Gromov–Witten variety of rational curves of degree $d$ in $X$ that meet three general points. We prove that, if this Gromov–Witten variety is rationally connected for all large degrees $d$, then the structure constants of the small quantum $K$-theory ring of $X$ vanish for large degrees.
quantum $K$ theory, rational connected varieties, Gromov–Witten variety
2010 Mathematics Subject Classification
Primary 14N35. Secondary 14M15, 14M20, 14M22, 14N15, 19E08.