A note on the Intersection of Veronese Surfaces

2003/02/14 by David Eisenbud, Klaus Hulek, Eisenbud, David +3
Mathematics · #13D02 #14J26 #14J45 #14N15 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:13D02 #msc:14J26 #msc:14J45 #msc:14N15

paper · pdf · doi:10.48550/arxiv.math/0302167

15 pages, AMS LaTeX

arxiv created 2003/02/14 · arxiv updated 2009/11/30

Abstract

Motivated by our study (elsewhere) of linear syzygies of homogeneous ideals generated by quadrics and their restrictions to subvarieties of the ambient projective space, we investigate in this note possible zero-dimensional intersections of two Veronese surfaces in P⁵. The case of two Veronese surfaces in P⁵ meeting in 10 simple points appears also in work of Coble, Conner and Reye in relation to the 10 nodes of a quartic symmetroid in P³, and we provide here a modern account for some of their results.

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