Dissertation/Thesis Abstract

Rational curves on universal hypersurfaces
by Staats, Charles, III, Ph.D., The University of Chicago, 2014, 86; 3638697
Abstract (Summary)

In this thesis, results are presented toward determining the number and dimension of irreducible components of the space of rational curves on a universal hypersurface. First, the question is reduced to classifying the strata of rational curves in projective space that are defined by the isomorphism class of the restriction of certain vector bundles. Partial results are given for describing these strata. Among these is a conjecture that the general stratum should have balanced isomorphism class. The conjecture is proved in a large infinite family of cases; in the course of the proof, a notion of a balanced vector bundle is introduced for reducible curves. Finally, these results are translated to give partial results about the original question.

A concrete picture of a few rational curves on universal hypersurfaces is given in the supplementary file animations.zip.

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Indexing (document details)
Advisor: Nori, Madhav V., Coskun, Izzet
Commitee:
School: The University of Chicago
Department: Mathematics
School Location: United States -- Illinois
Source: DAI-B 76/02(E), Dissertation Abstracts International
Source Type: DISSERTATION
Subjects: Mathematics
Keywords: Algebraic geometry, Moduli, Rational curves, Universal hypersurface
Publication Number: 3638697
ISBN: 9781321225204
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