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Berufserfahrung und Ausbildung
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SAP
Gesamte Berufserfahrung von Dr. Laura Tozzo anzeigen
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Veröffentlichungen
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Poincaré Series on Good Semigroup Ideals
Numerical Semigroups pp 351-367 (Part of the Springer INdAM Series book series (SINDAMS, volume 40))
The Poincaré series of a ring associated to a plane curve was defined by Campillo, Delgado, and Gusein-Zade. This series, defined through the value semigroup of the curve, encodes the topological information of the curve. In this paper we extend the definition of Poincaré series to the class of good semigroup ideals, to which value semigroups of curves belong. Using this definition we generalize a result of Pol: under suitable assumptions, given good semigroup ideals E and K, with K canonical…
The Poincaré series of a ring associated to a plane curve was defined by Campillo, Delgado, and Gusein-Zade. This series, defined through the value semigroup of the curve, encodes the topological information of the curve. In this paper we extend the definition of Poincaré series to the class of good semigroup ideals, to which value semigroups of curves belong. Using this definition we generalize a result of Pol: under suitable assumptions, given good semigroup ideals E and K, with K canonical, the Poincaré series of K − E is symmetric to the Poincaré series of E.
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Inverse limits of Macaulay’s inverse systems
Journal of Algebra Volume 525, 1 May 2019, Pages 341-358
Generalizing a result of Masuti and the second author, we describe inverse limits of Macaulay’s inverse systems for Cohen–Macaulay factor algebras of formal power series or polynomial rings over an infinite field. On the way we find a strictness result for filtrations defined by regular sequences. It generalizes
both a lemma of Uli Walther and the Rees isomorphism.Andere Autor:innen -
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Duality on Value Semigroups
J. Commut. Algebra Volume 11, Number 1 (2019), 81-129
We establish a combinatorial counterpart of the Cohen–Macaulay duality
on fractional ideals on curve singularities. To this end we consider the class of so–
called good semigroup ideals. Under suitable algebraic conditions it contains all value
semigroup ideals of fractional ideals. We give an intrinsic definition of canonical good
semigroup ideals and deduce a duality on good semigroup ideals. Canonical fractional
ideals are then characterized by having a canonical value…We establish a combinatorial counterpart of the Cohen–Macaulay duality
on fractional ideals on curve singularities. To this end we consider the class of so–
called good semigroup ideals. Under suitable algebraic conditions it contains all value
semigroup ideals of fractional ideals. We give an intrinsic definition of canonical good
semigroup ideals and deduce a duality on good semigroup ideals. Canonical fractional
ideals are then characterized by having a canonical value semigroup ideal. We prove
that the Cohen–Macaulay duality and our good semigroup duality are compatible under
taking values.Andere Autor:innen -
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The Structure of the Inverse System of Level K-Algebras
Collect. Math. 69 (2018), no. 3, 451–477
Macaulay's inverse system is an effective method to construct Artinian K-algebras with additional properties like, Gorenstein, level, more generally with any socle type. Recently, Elias and Rossi gave the structure of the inverse system of d-dimensional Gorenstein K-algebras for any d>0. In this paper we extend their result by establishing a one-to-one correspondence between d-dimensional level K-algebras and certain submodules of the divided power ring. We give several examples to…
Macaulay's inverse system is an effective method to construct Artinian K-algebras with additional properties like, Gorenstein, level, more generally with any socle type. Recently, Elias and Rossi gave the structure of the inverse system of d-dimensional Gorenstein K-algebras for any d>0. In this paper we extend their result by establishing a one-to-one correspondence between d-dimensional level K-algebras and certain submodules of the divided power ring. We give several examples to illustrate our result.
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Good subsemigroups of N^n
Internat. J. Algebra Comput. 28 (2018), no. 2, 179–206
We define the concept of good system of generators for good subsemigroups of $\mathbb N^n$. We show that minimal good systems of generators are unique for good subsemigroups of $\mathbb N^n$ and for good ideals. We give a constructive way to compute the canonical ideal and the Arf closure of a good subsemigroup of $\mathbb N^2$.
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A residual duality over Gorenstein rings with application to logarithmic differential forms
Journal of Singularities Volume 18 (2018), 272-299 (dedicated to the memory of Egbert Brieskorn)
Kyoji Saito's notion of a free divisor was generalized by the first author to reduced Gorenstein spaces and by Delphine Pol to reduced Cohen-Macaulay spaces. Starting point is the Aleksandrov-Terao theorem: A hypersurface is free if and only if its Jacobian ideal is maximal Cohen-Macaulay. Pol obtains a generalized Jacobian ideal as a cokernel by dualizing Aleksandrov's multi-logarithmic residue sequence. Notably it is essentially a suitably chosen complete intersection ideal that is used for…
Kyoji Saito's notion of a free divisor was generalized by the first author to reduced Gorenstein spaces and by Delphine Pol to reduced Cohen-Macaulay spaces. Starting point is the Aleksandrov-Terao theorem: A hypersurface is free if and only if its Jacobian ideal is maximal Cohen-Macaulay. Pol obtains a generalized Jacobian ideal as a cokernel by dualizing Aleksandrov's multi-logarithmic residue sequence. Notably it is essentially a suitably chosen complete intersection ideal that is used for dualizing. Pol shows that this generalized Jacobian ideal is maximal Cohen-Macaulay if and only if the module of Aleksandrov's multi-logarithmic differential k-forms has (minimal) projective dimension k-1, where k is the codimension in a smooth ambient space. This equivalent characterization reduces to Saito's definition of freeness in case k=1. In this article we translate Pol's duality result in terms of general commutative algebra. It yields a more conceptual proof of Pol's result and a generalization involving higher multi-logarithmic forms and generalized Jacobian modules.
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