Towards Characterizing Morphisms Between High Dimensional Hypersurfaces

Details Towards Characterizing Morphisms Between High Dimensional Hypersurfaces Towards Characterizing Morphisms Between High Dimensional Hypersurfaces

2003-01-31

arxiv.org/abs/math/0302005v1

Mathematics

Algebraic Geometry

15 pages, first paper of graduate thesis

Scientific paper

We show that for every morphism f between nonsingular hypersurfaces of dimension at least 3 and of general type in projective space, there is an everywhere defined endomorphism F of projective space that restricts to f. As a corollary, we see that if X,Y are nonsingular hypersurfaces of general type of dimension at least 3 such that there is a nonconstant morphism f from X to Y, then degY divides degX with quotient q, and moreover the endomorphism F of projective space is given by polynomials of degree q.

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