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pro vyhledávání: '"Vallès, Jean"'
We establish generalizations of Saito's criterion for the freeness of divisors in projective spaces that apply both to sequences of several homogeneous polynomials and to divisors on other complete varieties. As an application, the new criterion is a
Externí odkaz:
http://arxiv.org/abs/2407.14082
Saito gave a nice and efficient criterion to determine whether the module of logarithmic derivation associated with a reduced divisor in a complex variety is free or not. The aim of this note is to propose a new proof of this criterion, in the affine
Externí odkaz:
http://arxiv.org/abs/2402.08305
Autor:
Macinic, Anca, Vallès, Jean
We give a geometric characterisation of plus-one generated projective line arrangements that are next-to-free. We present new succinct proofs, via associated line bundles, for some properties of plus-one generated projective line arrangements.
Externí odkaz:
http://arxiv.org/abs/2309.10501
Publikováno v:
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY 56(7) 2024
Let $R=K[x,y,z]$. A reduced plane curve $C=V(f)\subset \mathbf P^2$ is $free \ $ if its associated module of tangent derivations $\mathrm{Der}(f)$ is a free $R$-module, or equivalently if the corresponding sheaf $T_ {\mathbf P^2 }(-\log C)$ of vector
Externí odkaz:
http://arxiv.org/abs/2306.09443
We define the notion of generalized logarithmic sheaves on a smooth projective surface, associated to a pair consisting of a reduced curve and some fixed points on it. We then set up the study of the Torelli property in this setting, focusing mostly
Externí odkaz:
http://arxiv.org/abs/2302.07632
We define logarithmic tangent sheaves associated with complete intersections in connection with Jacobian syzygies and distributions. We analyse the notions of local freeness, freeness and stability of these sheaves. We carry out a complete study of l
Externí odkaz:
http://arxiv.org/abs/2106.14453
Autor:
Marchesi, Simone, Vallès, Jean
In this paper we characterize the rank two vector bundles on $\mathbb{P}^2$ which are invariant under the actions of the parabolic subgroups $G_p:=\mathrm{Stab}_p(\mathrm{PGL}(3))$ fixing a point in the projective plane, $G_L:=\mathrm{Stab}_L(\mathrm
Externí odkaz:
http://arxiv.org/abs/2010.06506
Autor:
Ilardi, Giovanna, Vallès, Jean
Here we explain geometrically why the ideal I = (L 3 1 ,. .. , L 3 8) $\subset$ C[x 0 ,. .. , x 6 ] has the WLP in degree 3 and why it fails to have it in degree 5.
Externí odkaz:
http://arxiv.org/abs/1910.04035
Autor:
Marchesi, Simone, Vallès, Jean
Publikováno v:
Ãpijournal de Géométrie Algébrique, Volume 7 (May 2, 2023) epiga:7323
In this work we study line arrangements consisting in lines passing through three non-aligned points. We call them triangular arrangements. We prove that any combinatorics of a triangular arrangement is always realized by a Roots-of-Unity-Arrangement
Externí odkaz:
http://arxiv.org/abs/1903.08885
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