Zobrazeno 1 - 10
of 620
pro vyhledávání: '"32S40"'
Frenkel and Gross constructed a family of connections on $\mathbb{P}^1\backslash\{0,\infty\}$, for almost simple groups $\check{G}$ and their representations. In this article, we calculate the irregular Hodge numbers of these Frenkel--Gross connectio
Externí odkaz:
http://arxiv.org/abs/2412.05849
Autor:
Shi, Quan, Zuo, Huaiqing
Suppose $f = f_1^{b_1}...f_r^{b_r}\in \mathbb C[z_1,...,z_n]\setminus \mathbb C$. We introduce a variation of archimedean zeta function about $f_1,...,f_r$ and give a condition for generic existence of a type of poles. As an application, in the case
Externí odkaz:
http://arxiv.org/abs/2411.00757
Autor:
Tanabé, Susumu
We present a new topological method to study the discriminantal loci of an algebraic variety defined in a product of projective spaces. Our approach relies on an efficient use of groupoid to describe the monodromy. As an example, we treat here the di
Externí odkaz:
http://arxiv.org/abs/2409.16479
Autor:
Litt, Daniel
We survey some recent developments at the interface of algebraic geometry, surface topology, and the theory of ordinary differential equations. Motivated by "non-abelian" analogues of standard conjectures on the cohomology of algebraic varieties, we
Externí odkaz:
http://arxiv.org/abs/2409.02234
Autor:
Bath, Daniel, Dakin, Henry
We study the canonical Hodge filtration on the sheaf $\mathscr{O}_X(*D)$ of meromorphic functions along a divisor. For a germ of an analytic function $f$ whose Bernstein-Sato's polynomial's roots are contained in $(-2,0)$, we: give a simple algebraic
Externí odkaz:
http://arxiv.org/abs/2408.02601
Autor:
Eper, Miklos, Szabo, Szilard
We prove the Geometric P=W conjecture in rank 3 on the three-punctured sphere. We describe the topology at infinity of the related character variety. We use asymptotic abelianization of harmonic bundles away from the ramification divisor and an equiv
Externí odkaz:
http://arxiv.org/abs/2407.20638
Autor:
Steiner, Avi
We provide an alternative definition for the familiar concept of regular singularity for meromorphic connections. Our new formulation does not use derived categories, and it also avoids the necessity of finding a special good filtration as in the for
Externí odkaz:
http://arxiv.org/abs/2406.14253
We define a hypergeometric series in $m$ variables with $p+(p-1)m$ parameters, which reduces to the generalized hypergeometric series $_pF_{p-1}$ when $m=1$, and to Lauricella's hypergeometric series $F_C$ in $m$ variables when $p=2$. We give a syste
Externí odkaz:
http://arxiv.org/abs/2404.00295
Autor:
Wang, Haoxu
Claude Sabbah has defined the Fourier transform $G$ of the Gauss-Manin system for a non-degenerate and convenient Laurent polynomial and has shown that there exists a polarized mixed Hodge structure on the vanishing cycle of $G$. In this article, we
Externí odkaz:
http://arxiv.org/abs/2403.02105
Autor:
Bath, Daniel
We consider the Bernstein--Sato polynomial of a locally quasi-homogeneous polynomial $f \in R = \mathbb{C}[x_{1}, x_{2}, x_{3}]$. We construct, in the analytic category, a complex of $\mathscr{D}_{X}[s]$-modules that can be used to compute the $\math
Externí odkaz:
http://arxiv.org/abs/2402.08342