Towards characterizing morphims between high dimensional hypersurfaces
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52768723-MIT.pdf
Description
Full printable version
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1.92 MB
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Author(s)
Sheppard, David C. (David Christopher), 1977-
Advisor(s)
Aise Johan de Jong.
Date Issued
2003
Publisher
Massachusetts Institute of Technology
Abstract
This thesis is organized into two papers. All results are proven over an algebraically closed field of characteristic zero. Paper 1 concerns morphisms between hypersurfaces in Pn, n =/> 4. We show that if the two hypersurfaces involved in the morphism are of general type, then the morphism of hypersurfaces extends to an everywhere-defined endomorphism of Pn. A corollary is that if X [right arrow] Y is a nonconstant morphism of hypersurfaces of large dimension and large degree, then deg Y divides deg X. The main tool used to analyze morphism between hypersurfaces is an inequality of Chern classes analogous to the Hurwitz-inequality. Paper 2 is a long example. We check that every morphism from a quintic hypersurface in I4 to a nonsingular cubic hypersurface in P4 is constant. In the process, we classify morphisms froin the projective plane to nonsingular cubic threefolds.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003.
Includes bibliographical references (p. 44).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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