Initial ideals of tangent cones to Schubert varieties in orthogonal Grassmannians

2007/10/16 by K. N. Raghavan, Raghavan, K. N., Shyamashree Upadhyay +1
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Theories and Applications #Mathematics and Applications #math.AC #math.AG #math.CO #msc:05E15 #msc:13F50 #msc:13P10 #msc:14L35

paper · pdf · doi:10.48550/arxiv.0710.2950

36 pages, 3 figures; for version 2: error in definition of "new form" corrected

arxiv created 2008/03/16 · arxiv updated 2009/12/01

Abstract

We compute the initial ideals, with respect to certain conveniently chosen term orders, of ideals of tangent cones at torus fixed points to Schubert varieties in orthogonal Grassmannians. The initial ideals turn out to be square-free monomial ideals and therefore Stanley-Reisner face rings of simplicial complexes. We describe these complexes. The maximal faces of these complexes encode certain sets of non-intersecting lattice paths.

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