Towards characterizing morphims between high dimensional hypersurfaces

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2003

Author dc:creator

• Sheppard, David C. (David Christopher), 1977-

Advisor dc:contributor.advisor

• Aise Johan de Jong.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/29352

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/29352