2026-09-19T12:12:41Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/293522022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Aise Johan de Jong.
Sheppard, David C. (David Christopher), 1977-
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2005-10-14T20:01:18Z
2005-10-14T20:01:18Z
2003
2003
http://hdl.handle.net/1721.1/29352
52768723
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003.
Includes bibliographical references (p. 44).
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.
by David C. Sheppard.
Ph.D.
44 p.
2014696 bytes
2014504 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Towards characterizing morphims between high dimensional hypersurfaces
Thesis
application/pdf
Publication
unknown
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