Rational connectedness implies finiteness of quantum $K$-theory

Anders S. Buch (1) , Pierre-Emmanuel Chaput (2) , Leonardo C. Mihalcea (3) , Nicolas Perrin (4, 5)

1 Rutgers University, Department of Mathematics
2 IECL - Institut Élie Cartan de Lorraine
3 Department of Mathematics [Blacksburg]
4 HCM - Hausdorff Center for Mathematics
5 LMV - Laboratoire de Mathématiques de Versailles

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.

Mots clés: K-theorie

Domaines: Géométrie algébrique [math.AG]; Théorie des représentations [math.RT]

Anders S. Buch, Pierre-Emmanuel Chaput, Leonardo C. Mihalcea, Nicolas Perrin. Rational connectedness implies finiteness of quantum $K$-theory. Asian Journal of Mathematics, 2016, 20 (1), pp.117-122. ⟨10.4310/AJM.2016.v20.n1.a5⟩. ⟨hal-01297275⟩