352 research outputs found
Local cohomology of binomial edge ideals and their generic initial ideals
We provide a Hochster type formula for the local cohomology modules of binomial edge ideals. As a consequence we obtain a simple criterion for the CohenâMacaulayness and Buchsbaumness of these ideals and we describe their CastelnuovoâMumford regularity and their Hilbert series. Conca and Varbaro (Square-free Groebner degenerations, 2018) have recently proved a conjecture of Conca, De Negri and Gorla (J Comb Algebra 2:231â257, 2018) relating the graded components of the local cohomology modules of CartwrightâSturmfels ideals and their generic initial ideals. We provide an alternative proof for the case of binomial edge idealsPeer ReviewedPostprint (author's final draft
Castelnuovo-Mumford regularity of products of ideals
We discuss the behavior of the Castelnuovo-Mumford regularity under certain
operations on ideals and modules, like products or powers. In particular, we
show that reg(IM) can be larger than reg(M)+reg(I) even when I is an ideal of
linear forms and M is a module with a linear resolution. On the other hand, we
show that any product of ideals of linear forms has a linear resolution. We
also discuss the case of polymatroidal ideals and show that any product of
determinantal ideals of a generic Hankel matrix has a linear resolution.Comment: 14 page
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