Let V≅Cd+1 be a complex vector space. If one identifies it with a space of binary forms of degree d , then one gets an action of PGL(2) on any Grassmannian Gr(e+1,V). We will produce some refined numerical invariants for such an action that stratify the Grassmannian into irreducible and rational invariant strata. Assuming d≥3, the numerical invariants so obtained are shown to correspond in a simple way with the set of possible splitting types of the restricted tangent bundles of degree d rational curves C⊂Ps with s≤d−1. By means of the same techniques we produce explicit parameterizations for the varieties of rational curves with a given splitting type of the restricted tangent bundle.
PGL(2) actions on Grassmannians and projective construction of rational curves with given restricted tangent bundle
RE, Riccardo
2015-01-01
Abstract
Let V≅Cd+1 be a complex vector space. If one identifies it with a space of binary forms of degree d , then one gets an action of PGL(2) on any Grassmannian Gr(e+1,V). We will produce some refined numerical invariants for such an action that stratify the Grassmannian into irreducible and rational invariant strata. Assuming d≥3, the numerical invariants so obtained are shown to correspond in a simple way with the set of possible splitting types of the restricted tangent bundles of degree d rational curves C⊂Ps with s≤d−1. By means of the same techniques we produce explicit parameterizations for the varieties of rational curves with a given splitting type of the restricted tangent bundle.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.