Let V be a (d+1)-dimensional 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 G(e+1,V). We will produce some refined numerical invariants for such an action that stratify G(e+1,V) into irreducible and rational invariant strata. Assuming d≥3, the invariants so obtained are shown to correspond with the set of possible splitting types of the restricted tangent bundles of degree d rational curves in P^s with s ≤d-1.
PGL(2) actions on Grassmannians and projective construction of rational curves with given restricted tangent bundle / A. Alzati, R. Re. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 219:5(2015 May), pp. 1320-1335. [10.1016/j.jpaa.2014.06.007]
PGL(2) actions on Grassmannians and projective construction of rational curves with given restricted tangent bundle
A. AlzatiPrimo
;
2015
Abstract
Let V be a (d+1)-dimensional 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 G(e+1,V). We will produce some refined numerical invariants for such an action that stratify G(e+1,V) into irreducible and rational invariant strata. Assuming d≥3, the invariants so obtained are shown to correspond with the set of possible splitting types of the restricted tangent bundles of degree d rational curves in P^s with s ≤d-1.File | Dimensione | Formato | |
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