Normal bundles of lines on hypersurfaces

2017/05/04 by Larson, Hannah · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.01972

Abstract

Let X ⊂ ℙⁿ be a smooth hypersurface. Given a sequence of integers a = (a₁, …, a_n-2) with a₁ ≤ ⋯ ≤ a_n-2, let F_a(X) be the parameter space of lines L on X such that N_L/X ≅ O(a₁) ⊕ ⋯ ⊕ O(a_n-2). The loci F_a(X) form a stratification of the Fano scheme of lines on X. We show that for general hypersurfaces, the F_a(X) have the expected dimension and, in this case, compute the class of F_a(X) in the Chow ring of the Grassmannian of lines in ℙⁿ. For certain splitting types a, we also provide non-trivial upper bounds on the dimension of F_a(X) that hold for all smooth X.

Cited by

• Restricted tangent bundle of rational curves on projective hypersurfaces
• A derived category analogue of the Nakai--Moishezon criterion

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