Bounds for the Betti numbers of successive stellar subdivisions of a simplex
Abstract
We give a bound for the Betti numbers of the StanleyReisner ring of a stellar subdivision of a Gorenstein* simplicial complex by applying unprojection theory. From this we derive a bound for the Betti numbers of iterated stellar subdivisions of the boundary complex of a simplex. The bound depends only on the number of subdivisions, and we construct examples which prove that it is sharp.
 Publication:

arXiv eprints
 Pub Date:
 December 2012
 arXiv:
 arXiv:1212.4358
 Bibcode:
 2012arXiv1212.4358B
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Combinatorics;
 13F55 (Primary) 13D02;
 13P20;
 13H10 (Secondary)
 EPrint:
 15 pages, no figures. Package may be downloaded at http://www.mathematik.unikl.de/~boehm/Macaulay2/BettiBounds/html/