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Very free rational curves in Fano varieties
- Publication Year :
- 2021
-
Abstract
- 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.<br />Comment: 18 pages
- Subjects :
- Mathematics - Algebraic Geometry
14H60, 14G17 (Primary) 14J45, 14N25 (Secondary)
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2106.01991
- Document Type :
- Working Paper