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March 2021 Normal Bundles of Lines on Hypersurfaces
Hannah K. Larson
Michigan Math. J. 70(1): 115-131 (March 2021). DOI: 10.1307/mmj/1586419412

Abstract

If X is a smooth hypersurface in complex projective space, the Fano variety of lines on X is stratified by the splitting type of the normal bundle of the line. We show that for general hypersurfaces, these strata have the expected dimension and, in this case, compute the class of the closure of the strata in the Chow ring of the Grassmannian of lines in projective space. For certain splitting types, we also provide upper bounds on the dimension of the strata that hold for all smooth X.

Citation

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Hannah K. Larson. "Normal Bundles of Lines on Hypersurfaces." Michigan Math. J. 70 (1) 115 - 131, March 2021. https://doi.org/10.1307/mmj/1586419412

Information

Received: 13 December 2018; Revised: 8 August 2019; Published: March 2021
First available in Project Euclid: 9 April 2020

Digital Object Identifier: 10.1307/mmj/1586419412

Subjects:
Primary: 14H60, 14J70, 14N20

Rights: Copyright © 2021 The University of Michigan

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Vol.70 • No. 1 • March 2021
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