Zobrazeno 1 - 10
of 177
pro vyhledávání: '"Reichelt, Thomas"'
We consider $A$-hypergeometric (or GKZ-)systems in the case where the grading (character) group is an arbitrary finitely generated Abelian group. Emulating the approach taken for classical GKZ-systems in arXiv:math/0406383 that allows for a coefficie
Externí odkaz:
http://arxiv.org/abs/2402.00762
Many hypergeometric differential systems that arise from a geometric setting can be endowed with the structure of mixed Hodge modules. We generalize this fundamental result to the tautological systems associated to homogeneous spaces by giving a func
Externí odkaz:
http://arxiv.org/abs/2211.05356
We show that the sum of the local cohomological dimension and the rectified $\mathbb Q$-homological depth of a closed analytic subspace of a complex manifold coincide with the dimension of the ambient manifold. The local cohomological dimension is th
Externí odkaz:
http://arxiv.org/abs/2108.12896
We discuss for an affine variety $Y$ embedded in affine space $X$ two sets of integers attached to $Y\subseteq X$ via local and de Rham cohomology spectral sequences. We give topological interpretations, study them in small dimension, and investigate
Externí odkaz:
http://arxiv.org/abs/2106.04457
We review some classical and modern aspects of hypergeometric differential equations, including $A$-hypergeometric systems of Gel'fand, Graev, Kapranov and Zelevinsky. Some recent advances in this theory, such as Euler-Koszul homology, rank jump phen
Externí odkaz:
http://arxiv.org/abs/2004.07262
Autor:
Reichelt, Thomas, Walther, Uli
If $\beta\in\CC^d$ is integral but not a strongly resonant parameter for the homogeneous matrix $A\in\ZZ^{d\times n}$ with $\ZZ A=\ZZ^d$, then the associated GKZ-system carries a naturally defined mixed Hodge module structure. We study here in the no
Externí odkaz:
http://arxiv.org/abs/1809.04247
We construct complex projective schemes with Lyubeznik numbers of their cones depending on the choices of projective embeddings. This answers a question of G. Lyubeznik in the characteristic 0 case. It contrasts with a theorem of W. Zhang in the posi
Externí odkaz:
http://arxiv.org/abs/1803.07448
Publikováno v:
Alg. Number Th. 13 (2019) 1415-1442
We show that certain one-dimensional hypergeometric differential systems underlie objects of the category of irregular mixed Hodge modules, which was recently introduced by Sabbah, and compute the irregular Hodge filtration for them. We also provide
Externí odkaz:
http://arxiv.org/abs/1803.04886
Publikováno v:
In Topology and its Applications 15 May 2022 313
Autor:
Reichelt, Thomas, Walther, Uli
In this note we study families of Gauss-Manin systems arising from Laurent polynomials with parametric coefficients under projection to the parameter space. For suitable matrices of exponent vectors, we exhibit a natural four-term exact sequence for
Externí odkaz:
http://arxiv.org/abs/1703.03057