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# Documents  Dimca, Alexandru | enregistrements trouvés : 5

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## Hodge theory and syzygies of the Jacobian ideal Dimca, Alexandru | CIRM H

Multi angle

Research talks;Algebraic and Complex Geometry

Let $f$ be a homogeneous polynomial, defining a principal Zariski open set $D(f)$ in some complex projective space $\mathbb{P}^n$ and a Milnor fiber $F(f)$ in the affine space $\mathbb{C}^{n+1}$. Let $f_0, . . . , f_n$ denote the partial derivatives of $f$ with respect to $x_0, . . . , x_n$ and consider syzygies $a_0f_0 + a_1f1 + a_nf_n = 0$, where $a_j$ are homogeneous polynomials of the same degree $k$.
Using the mixed Hodge structure on $D(f)$ and $F(f)$, one can obtain information on the possible values of $k$.
Let $f$ be a homogeneous polynomial, defining a principal Zariski open set $D(f)$ in some complex projective space $\mathbb{P}^n$ and a Milnor fiber $F(f)$ in the affine space $\mathbb{C}^{n+1}$. Let $f_0, . . . , f_n$ denote the partial derivatives of $f$ with respect to $x_0, . . . , x_n$ and consider syzygies $a_0f_0 + a_1f1 + a_nf_n = 0$, where $a_j$ are homogeneous polynomials of the same degree $k$.
Using the mixed Hodge structure on ...

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## A computational approach to Milnor fiber cohomology Dimca, Alexandru | CIRM H

Multi angle

Research talks;Algebraic and Complex Geometry

In this talk we consider the Milnor fiber F associated to a reduced projective plane curve $C$. A computational approach for the determination of the characteristic polynomial of the monodromy action on the first cohomology group of $F$, also known as the Alexander polynomial of the curve $C$, is presented. This leads to an effective algorithm to detect all the roots of the Alexander polynomial and, in many cases, explicit bases for the monodromy eigenspaces in terms of polynomial differential forms. The case of line arrangements, where there are many open questions, will illustrate the complexity of the problem. These results are based on joint work with Morihiko Saito, and with Gabriel Sticlaru. In this talk we consider the Milnor fiber F associated to a reduced projective plane curve $C$. A computational approach for the determination of the characteristic polynomial of the monodromy action on the first cohomology group of $F$, also known as the Alexander polynomial of the curve $C$, is presented. This leads to an effective algorithm to detect all the roots of the Alexander polynomial and, in many cases, explicit bases for the ...

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## Topics on real and complex singularities :an introduction Dimca, Alexandru | Friedr. Vieweg & Sohn 1987

Ouvrage

- 242 p.
ISBN 978-3-528-08999-3

Localisation : Ouvrage RdC (DIMC)

singularité # singularité complexe # théorie de la simplicité

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## Singularities and topology of hypersurfaces Dimca, Alexandru | Springer-Verlag 1992

Ouvrage

ISBN 978-0-387-97709-6

Universitext

Localisation : Disparu;Ouvrage RdC (DIMC)

hypersurface # singularité # topologie algébrique

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## Sheaves in topology Dimca, Alexandru | Springer 2004

Ouvrage

- 236 p.
ISBN 978-3-540-20665-1

Universitext

Localisation : Ouvrage RdC (DIMC)

topologie # méthode transcendentale # singularité # cohomologie # faisceau # faisceau constructible # coefficient de faisceau # catégorie dérivée # faisceau complexe # dualité de Verdier # D-module

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