A note on r hypersurfaces intersecting in ℙ^r

2019/08/05 by Dennis Tseng, Tseng, Dennis
Mathematics · #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #Meromorphic and Entire Functions #math.AG #msc:14J70

paper · pdf · doi:10.48550/arxiv.1908.01620

6 pages, comments welcome

arxiv created 2019/08/05 · arxiv updated 2019/08/06

Abstract

We consider the locus of r-tuples of homogeneous forms of some fixed degree whose common vanishing locus in ℙ^r is positive dimensional. We show that any component of maximal dimension of that locus either consists of homogeneous forms all vanishing on some line or homogeneous forms where a proper subset fail to intersect properly.

Related

• Collections of hypersurfaces containing a curve
• On the contravariant of homogeneous forms arising from isolated hypersurface singularities
• Hypersurfaces passing through the Galois orbit of a point
• Refined intersection products and limiting linear subspaces of hypersurfaces
• Forms representing forms: The definite case