Rational curves on minuscule Schubert varieties
| dc.creator | Perrin, Nicolas | |
| dc.date | 2004-07-08 | |
| dc.date.accessioned | 2026-07-07T05:10:04Z | |
| dc.date.available | 2026-07-07T05:10:04Z | |
| dc.description | Let X be a minuscule Schubert variety and $α$ a class of 1-cycle on X. In this article we describe the irreducible components of the scheme of morphisms of class $α$ from a rational curve to X. The irreducible components are described in the following way : the class $α$ can be seen as an element of $Pic(X)^*$ the dual of the Picard group. Because any Weil-divisor need not to be a Cartier-divisor, there is (only) a surjective map $s:A^1(X)^*\to Pic(X)^*$ from the dual of the group of codimension 1 cycles to the dual of the Picard group. The irreducible components are given by the effective elements $β$ in $A^1(X)^*$ such that $s(β)=α$. The proof of the result uses the Bott-Samelson resolution Y of X. We prove that any curve on X can be lifted in Y (after deformation). This is because any divisor on minuscule Schubert variety is a moving one. Then we prove that any curve coming from X can be deformed so that it does not meet the contracted divisor of $Y\to X$. This is possible because for minuscule Schubert variety there are lines in the projectivised tangent space to a singularity. It is now sufficient to deal with the case of the orbit of $Stab(X)$ the stabiliser of X and we can apply results of our previous paper math.AG/0003199. | |
| dc.description | In english, 29 pages | |
| dc.identifier | https://arxiv.org/abs/math/0407123 | |
| dc.identifier | http://arxiv.org/abs/math/0407123 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71814 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Rational curves on minuscule Schubert varieties | |
| dc.type | text |