Collections of hypersurfaces containing a curve

2017/02/21 by Dennis Tseng, Tseng, Dennis
Mathematics · #14G15 #14H10 #14J10 #14J70 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14G15 #msc:14H10 #msc:14J10 #msc:14J70

paper · pdf · doi:10.48550/arxiv.1702.06517

37 pages, incorporated suggestions by referees, final version, comments welcome

arxiv created 2018/06/28 · arxiv updated 2018/06/29

Abstract

We consider the closed locus of r-tuples of hypersurfaces in ℙ^r with positive dimensional intersection, and show in a large range of degrees that its largest component is the locus of r-tuples of hypersurfaces whose intersection contains a line. We then apply our methods to obtain new results on the largest components of the locus of hypersurfaces with positive dimensional singular loci and the locus of smooth hypersurfaces with a higher dimensional family of lines through a point than expected.

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