Let V congruent to 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 subset of P-s 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. (C) 2014 Elsevier B.V. All rights reserved.

PGL(2) actions on Grassmannians and projective construction of rational curves with given restricted tangent bundle

Re, R.
2015-01-01

Abstract

Let V congruent to 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 subset of P-s 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. (C) 2014 Elsevier B.V. All rights reserved.
2015
http://www.elsevier.com/locate/jpaa
Algebra and Number Theory
Alzati, A.; Re, R.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2067714
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