2004/05/13 by Abdelmalek Abdesselam, Abdesselam, Abdelmalek, Jaydeep Chipalkatti +1
Mathematics · Physics and Astronomy · #05A15 #14F17 #14L35 #81T18 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Representation Theory (math.RT) #gr-qc #hep-th #math.AG #math.CO #math.RT #msc:05A15 #msc:14F17 #msc:14L35 #msc:81T18
paper · pdf · doi:10.48550/arxiv.math/0405236
LaTeX, 27 pages
arxiv created 2004/05/13 · arxiv updated 2009/12/01
Let n,d be positive integers, with d even (say d=2e). Let X_(n,d) denote the locus of degree d hypersurfaces in Pn which consist of two e-fold hyperplanes. We bound the regularity of the ideal of this variety. Moreover, we show that this variety is r-normal for r at least 2. The proof of the latter part is is a result of a tripartite collaboration of algebraic geometry, classical invariant theory and theoretical physics. It is executed by reducing the question to a combinatorial calculation involving Feynman diagrams and hypergeometric functions.