University of Illinois Chicago
Browse

Very free rational curves in Fano varieties

Download (332.06 kB)
journal contribution
posted on 2023-04-12, 22:25 authored by Izzet CoskunIzzet Coskun, Geoffrey Smith
Let X be a projective variety and let C be a rational normal curve on X. We compute the normal bundle of C in a general complete intersection of hypersurfaces of sufficiently large degree in X. As a result, we establish the separable rational connectedness of a large class of varieties, including general Fano complete intersections of hypersurfaces of degree at least three in flag varieties, in arbitrary characteristic. In addition, we give a new way of computing the normal bundle of certain rational curves in products of varieties in terms of their restricted tangent bundles and normal bundles on each factor.

Funding

Birational Geometry of Moduli Spaces and Bridgeland Stability | Funder: National Science Foundation | Grant ID: DMS-1500031

FRG: Collaborative Research: Bridgeland Stability, Moduli Spaces and Birational Geometry | Funder: National Science Foundation | Grant ID: DMS-1664296

History

Citation

Coskun, I.Smith, G. (2022). Very free rational curves in Fano varieties. Journal of Algebra, 611, 246-264. https://doi.org/10.1016/j.jalgebra.2022.08.009

Publisher

Elsevier

Language

  • en

issn

0021-8693

Usage metrics

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC