En poursuivant votre navigation sur ce site, vous acceptez l'utilisation d'un simple cookie d'identification. Aucune autre exploitation n'est faite de ce cookie. OK

Documents 32S35 4 results

Filter
Select: All / None
Q
Déposez votre fichier ici pour le déplacer vers cet enregistrement.
y

Hodge conjecture for singular varieties - Kaur, Inder (Author of the conference) | CIRM H

Multi angle

The classical Hodge conjecture for smooth, projective varieties has been open for over 70 years, although it has been proven for some specific varieties. In this talk I will discuss a cohomological version of the Hodge conjecture for singular varieties. I will give a sufficient condition in terms of Mumford-Tate groups for a variety to satisfy the singular Hodge conjecture. If time allows I will give explicit examples of such varieties. This is joint work with Ananyo Dan.[-]
The classical Hodge conjecture for smooth, projective varieties has been open for over 70 years, although it has been proven for some specific varieties. In this talk I will discuss a cohomological version of the Hodge conjecture for singular varieties. I will give a sufficient condition in terms of Mumford-Tate groups for a variety to satisfy the singular Hodge conjecture. If time allows I will give explicit examples of such varieties. This is ...[+]

14C30 ; 32S35

Bookmarks Report an error
Déposez votre fichier ici pour le déplacer vers cet enregistrement.
y

Hodge theory and syzygies of the Jacobian ideal - Dimca, Alexandru (Author of the conference) | CIRM H

Multi angle

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 ...[+]

14B05 ; 13D02 ; 32S35

Bookmarks Report an error
Déposez votre fichier ici pour le déplacer vers cet enregistrement.
y
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 ...[+]

32S55 ; 32S35 ; 32S22

Bookmarks Report an error
Déposez votre fichier ici pour le déplacer vers cet enregistrement.
y

Hodge filtration and birational geometry - Popa, Mihnea (Author of the conference) | CIRM H

Multi angle

I will give a general introduction to the study of the Hodge filtration on local cohomology sheaves associated to closed subschemes of smooth complex varieties, using techniques from both D-module theory and birational geometry. In the case of hypersurfaces, this is essentially the theory of Hodge ideals, which I will recall. This study has applications to various topics, like local vanishing, local cohomological dimension, the Du Bois complex, minimal exponents of singularities, etc. I will discuss a few, and more will appear in M. Mustaja's lecture.[-]
I will give a general introduction to the study of the Hodge filtration on local cohomology sheaves associated to closed subschemes of smooth complex varieties, using techniques from both D-module theory and birational geometry. In the case of hypersurfaces, this is essentially the theory of Hodge ideals, which I will recall. This study has applications to various topics, like local vanishing, local cohomological dimension, the Du Bois complex, ...[+]

14B05 ; 14F10 ; 32S35 ; 14F17

Bookmarks Report an error