Linear syzygies, flag complexes, and regularity

• Autores: Alexandru Constantinescu, Thomas Kahle, Matteo Varbaro
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 67, Fasc. 3, 2016, págs. 357-362
• Idioma: inglés
• DOI: 10.1007/s13348-015-0141-3
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• Resumen

  • We show that for every ?∈ℤ>0 there exist monomial ideals generated in degree two, with linear syzygies, and regularity of the quotient equal to ? . For Gorenstein ideals we prove that the regularity of their quotients can not exceed four, thus showing that for ?>4 every triangulation of a ? -manifold has a hollow square or simplex. We also show that for most monomial ideals generated in degree two and with linear syzygies the regularity is ?(log(log(?)) , where ? is the number of variables.