2003/01/31 by David Sheppard, Sheppard, David
Mathematics · #14J30 #14J70 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #math.AG #msc:14J30 #msc:14J70
paper · pdf · doi:10.48550/arxiv.math/0302005
15 pages, first paper of graduate thesis
arxiv created 2003/01/31 · openalex publication_date 2003/01/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.