We give a bound for the Betti numbers of the Stanley-Reisner 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.
- Pub Date:
- December 2012
- Mathematics - Commutative Algebra;
- Mathematics - Combinatorics;
- 13F55 (Primary) 13D02;
- 13H10 (Secondary)
- 15 pages, no figures. Package may be downloaded at http://www.mathematik.uni-kl.de/~boehm/Macaulay2/BettiBounds/html/