Numerically Testing Generically Reduced Projective Schemes for the Arithmetic Gorenstein Property
نویسندگان
چکیده
Let X ⊂ P be a generically reduced projective scheme. A fundamental goal in computational algebraic geometry is to compute information about X even when defining equations for X are not known. We use numerical algebraic geometry to develop a test for deciding if X is arithmetically Gorenstein and apply it to three secant varieties.
منابع مشابه
Glicci Ideals
A central problem in liaison theory is to decide whether every arithmetically Cohen-Macaulay subscheme of projective n-space can be linked by a finite number of arithmetically Gorenstein schemes to a complete intersection. We show that this can be indeed achieved if the given scheme is also generically Gorenstein and we allow the links to take place in an (n + 1)-dimensional projective space. F...
متن کاملAmalgamated duplication of some special rings along an ideal
Let be a commutative Noetherian ring and let I be a proper ideal of . D’Anna and Fontana in [6] introduced a new construction of ring, named amalgamated duplication of along I. In this paper by considering the ring homomorphism , it is shown that if , then , also it is proved that if , then there exists such that . Using this result it is shown that if is generically Cohen-Macaulay (resp. gen...
متن کاملGorenstein projective objects in Abelian categories
Let $mathcal {A}$ be an abelian category with enough projective objects and $mathcal {X}$ be a full subcategory of $mathcal {A}$. We define Gorenstein projective objects with respect to $mathcal {X}$ and $mathcal{Y}_{mathcal{X}}$, respectively, where $mathcal{Y}_{mathcal{X}}$=${ Yin Ch(mathcal {A})| Y$ is acyclic and $Z_{n}Yinmathcal{X}}$. We point out that under certain hypotheses, these two G...
متن کاملReduced Arithmetically Gorenstein Schemes and Simplicial Polytopes with Maximal Betti Numbers
An SI-sequence is a finite sequence of positive integers which is symmetric, unimodal and satisfies a certain growth condition. These are known to correspond precisely to the possible Hilbert functions of Artinian Gorenstein algebras with the Weak Lefschetz Property, a property shared by most Artinian Gorenstein algebras. Starting with an arbitrary SI-sequence, we construct a reduced, arithmeti...
متن کاملNoncommutative Gorenstein Projective Schemes and Gorenstein-injective Sheaves
We prove that if a positively-graded ring R is Gorenstein and the associated torsion functor has finite cohomological dimension, then the corresponding noncommutative projective scheme Tails(R) is a Gorenstein category in the sense of [10]. Moreover, under this condition, a (right) recollement relating Gorensteininjective sheaves in Tails(R) and (graded) Gorenstein-injective R-modules is given.
متن کامل