Maximal disjoint Schubert cycles in Rational Homogeneous spaces

Abstract: In 1974 Tango proved that there are no non-constant morphisms from $lmathbb{P}^n$ to the Grassmannian $G(l,m)$ if $n > m$; similar results were later obtained for morphisms from other Fano manifolds to Grassmannians. In this talk I will present the following generalization of these results: if $X$ and $Y$ are rational homogeneous manifold obtained as quotients of classical groups $G_X$ and $G_Y$ of the same type and $rk(G_X) > rk(G_Y)$ then there are no non-constant morphisms from $X$ to $Y$. The key ingredient of the proof is the determination of the effective good divisibility of rational homogeneous manifolds of classical type, that is, the greatest integer $s$ such that two effective cycles in the Chow ring whose sum of codimensions is $s$ have nonzero intersection. This talk is based on a joint work with R. Muñoz and L.E. Solá Conde.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html