Open Collections

On vanishing patterns in Betti tables of edge ideals

Banff International Research Station for Mathematical Innovation and Discovery

Many important invariants of ideals in a polynomial ring can be read off from the locations of the zeros in their corresponding Betti table, for example the regularity, projective dimension, etc. We consider two problems on Betti tables of monomial ideals generated in degree 2 (edge ideals, after polarization): 1. Strand connectivity: can rows in the Betti table have internal zeros? [Conca, Weildon] 2. Subadditivity: for ti the maximal j for which "i,j is nonzero, must ta+b <= ta + tb? [Herzog-Srinivasan, Avramov-Conca-Iyengar] We show that for the first question the answer is NO for the first 2 rows and YES otherwise. We use it in showing that for the second question the answer is YES for b = 1, 2, 3 (for b = 1 this was proved by Herzog-Srinivasan, for all monomial ideals). Via Hochster formula, our proofs are topological-combinatorial.

Mathematics; Commutative rings and algebras; Several complex variables and analytic spaces; Commutative algebra

video/mp4

Author affiliation: The Hebrew University of Jerusalem

2016-09-13

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59155

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/