English

A regularity result for a locus of Brill type

Algebraic Geometry 2009-09-29 v1 General Relativity and Quantum Cosmology High Energy Physics - Theory Combinatorics Representation Theory

Abstract

Let n,d be positive integers, with d even (say d=2e). Let X_(n,d) denote the locus of degree d hypersurfaces in P^n 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.

Keywords

Cite

@article{arxiv.math/0405236,
  title  = {A regularity result for a locus of Brill type},
  author = {Abdelmalek Abdesselam and Jaydeep Chipalkatti},
  journal= {arXiv preprint arXiv:math/0405236},
  year   = {2009}
}

Comments

LaTeX, 27 pages

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