Local cohomology of binomial edge ideals and their generic initial ideals

• Autores: Josep Àlvarez Montaner
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 71, Fasc. 2, 2020, págs. 331-348
• Idioma: inglés
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• Resumen

  • 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 Cohen–Macaulayness and Buchsbaumness of these ideals and we describe their Castelnuovo–Mumford 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 2:231–257, 2018) relating the graded components of the local cohomology modules of Cartwright–Sturmfels ideals and their generic initial ideals. We provide an alternative proof for the case of binomial edge ideals.