2012
DOI: 10.1007/s13348-012-0076-x
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Gorenstein algebras presented by quadrics

Abstract: We establish restrictions on the Hilbert function of standard graded Gorenstein algebras with only quadratic relations. Furthermore, we pose some intriguing conjectures and provide evidence for them by proving them in some cases using a number of different techniques, including liaison theory and generic initial ideals.

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Cited by 21 publications
(32 citation statements)
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References 24 publications
(60 reference statements)
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“…An immediate consequence of the proposition above significantly extends the Injectivity Lemma of Proposition 4.3 of [5], proved in that paper in the case d = 2.…”
Section: Stratifications Of I Dsupporting
confidence: 74%
“…An immediate consequence of the proposition above significantly extends the Injectivity Lemma of Proposition 4.3 of [5], proved in that paper in the case d = 2.…”
Section: Stratifications Of I Dsupporting
confidence: 74%
“…In this way we construct a concrete family of algebras presented by quadrics and whose Hilbert vector is non unimodal. These algebras provide counterexamples for two conjectures posed in [MN1,MN2].…”
Section: Introductionmentioning
confidence: 92%
“…In [MN2], the authors studied Artinian Gorenstein algebras presented by quadrics, they provided some constructions of such algebras and described their possible Hilbert vectors in low codimension. In [MN1] and [MN2] the authors proposed two conjectures.…”
Section: Introductionmentioning
confidence: 99%
“…In recent times the first author, in [Go], constructed families of algebras failing WLP. We recall the following result: On the other hand, for algebras presented by quadrics there was a conjecture posed in [MN1,MN2]:…”
Section: Algebras Presented By Quadricsmentioning
confidence: 99%
“…We also construct new examples of Artinian Gorenstein algebras presented by quadrics that does not satisfy the Weak Lefschetz Property (WLP); we construct minimal examples of such algebras and we give bounds, depending on the degree, for their existence. Artinian Gorenstein algebras presented by quadrics were conjectured to satisfy WLP in [MN1,MN2], and in a previous paper we construct the first counter-examples (see [GZ]). *Partially supported by the CAPES postdoctoral fellowship, Proc.…”
mentioning
confidence: 99%