Search results for " Gorenstein"

showing 3 items of 3 documents

The ideal duplication

2021

AbstractIn this paper we present and study the ideal duplication, a new construction within the class of the relative ideals of a numerical semigroup S, that, under specific assumptions, produces a relative ideal of the numerical duplication $$S\bowtie ^b E$$ S ⋈ b E . We prove that every relative ideal of the numerical duplication can be uniquely written as the ideal duplication of two relative ideals of S; this allows us to better understand how the basic operations of the class of the relative ideals of $$S\bowtie ^b E$$ S ⋈ b E work. In particular, we characterize the ideals E such that $$S\bowtie ^b E$$ S ⋈ b E is nearly Gorenstein.

Class (set theory)Pure mathematicsAlgebra and Number TheoryIdeal (set theory)Nearly Gorenstein semigroups010102 general mathematics0102 computer and information sciences01 natural sciencesNearly Gorenstein semigroups Numerical duplication Relative ideal Canonical idealSettore MAT/02 - Algebra010201 computation theory & mathematicsNumerical semigroupNumerical duplicationRelative idealCanonical ideal0101 mathematicsAlgebra over a fieldMathematics
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Rational normal curves and Hadamard products

2021

AbstractGiven $$r>n$$ r > n general hyperplanes in $$\mathbb P^n,$$ P n , a star configuration of points is the set of all the n-wise intersection of the hyperplanes. We introduce contact star configurations, which are star configurations where all the hyperplanes are osculating to the same rational normal curve. In this paper, we find a relation between this construction and Hadamard products of linear varieties. Moreover, we study the union of contact star configurations on a same conic in $$\mathbb P^2$$ P 2 , we prove that the union of two contact star configurations has a special h-vector and, in some cases, this is a complete intersection.

Hadamard productGeneral Mathematics13C40 13C70 14M10 14M99 14N20Astrophysics::Cosmology and Extragalactic AstrophysicsMathematics - Commutative AlgebraCommutative Algebra (math.AC)Complete intersection Hadamard product Star configuration GorensteinSettore MAT/02 - AlgebraMathematics - Algebraic GeometryComplete intersection Hadamard product star configuration Gorenstein.FOS: MathematicsStar configurationAstrophysics::Solar and Stellar AstrophysicsSettore MAT/03 - GeometriaAstrophysics::Earth and Planetary AstrophysicsAlgebraic Geometry (math.AG)Complete intersectionAstrophysics::Galaxy AstrophysicsGorenstein
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The nearly Gorenstein property for numerical duplications and semitrivial extensions

2022

In this thesis we present and study the ideal duplication, a new construction within the class of the relative ideals of a numerical semigroup $S$, that, under specific assumptions, produces a relative ideal of the numerical duplication $SJoin^b E$, for some ideal $E$ of $S$. We prove that every relative ideal of the numerical duplication can be uniquely written as the ideal duplication of two relative ideals of $S$; this allows us to better understand how the basic operations of the class of the relative ideals of $SJoin^b E$ work. In particular, we characterize the ideals $E$ such that $SJoin^b E$ is nearly Gorenstein. With the aim to generalize this construction to commutative rings with…

Ideal DuplicationSettore MAT/02 - AlgebraNagata's IdealizationNumerical SemigroupNearly Gorenstein Numerical SemigroupSemitrivial ExtensionNearly Gorenstein RingRelative IdealZ_2-Graded RingCanonical IdealNumerical Duplication
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