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.
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