Zobrazeno 1 - 10
of 29
pro vyhledávání: '"Bath, Daniel"'
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:
Bath, Daniel, Walther, Uli
Given a matroid or flag of matroids we introduce several broad classes of polynomials satisfying Deletion-Contraction identities, and study their singularities. There are three main families of polynomials captured by our approach: matroidal polynomi
Externí odkaz:
http://arxiv.org/abs/2404.07885
Autor:
Bath, Daniel
We consider the Bernstein--Sato polynomial of a polynomial $f \in R = \mathbb{C}[x_{1}, x_{2}, x_{3}]$ that analytically locally everywhere admits a positively weighted homogeneous defining equation. We construct, in the analytic category, a complex
Externí odkaz:
http://arxiv.org/abs/2402.08342
Autor:
Bath, Daniel1 dan.bath@kuleuven.be
Publikováno v:
Forum of Mathematics, Pi. 11/6/2024, Vol. 12, p1-45. 45p.
Autor:
Bath, Daniel, Saito, Morihiko
For a rank 1 local system on the complement of a reduced divisor on a complex manifold $X$, its cohomology is calculated by the twisted meromorphic de Rham complex. Assuming the divisor is everywhere positively weighted homogeneous, we study necessar
Externí odkaz:
http://arxiv.org/abs/2203.11716
Autor:
Bath, Daniel
For a reduced hyperplane arrangement we prove the analytic Twisted Logarithmic Comparison Theorem, subject to mild combinatorial arithmetic conditions on the weights defining the twist. This gives a quasi-isomorphism between the twisted logarithmic d
Externí odkaz:
http://arxiv.org/abs/2202.01462
Autor:
Bath, Daniel
We present a variant of the Peskine--Szpiro Acyclicity Lemma, and hence a way to certify exactness of a complex of finite modules over a large class of (possibly) noncommutative rings. Specifically, over the class of Auslander regular rings. In the c
Externí odkaz:
http://arxiv.org/abs/2109.14223
Autor:
Bath, Daniel
For strongly Euler-homogeneous, Saito-holonomic, and tame analytic germs we consider general types of multivariate Bernstein-Sato ideals associated to arbitrary factorizations of our germ. We show the zero loci of these ideals are purely codimension
Externí odkaz:
http://arxiv.org/abs/2008.07447
Autor:
Bath, Daniel
For a central, not necessarily reduced, hyperplane arrangement $f$ equipped with any factorization $f = f_{1} \cdots f_{r}$ and for $f^{\prime}$ dividing $f$, we consider a more general type of Bernstein--Sato ideal consisting of the polynomials $B(S
Externí odkaz:
http://arxiv.org/abs/1909.00547
Autor:
Bath, Daniel
Given a complex germ $f$ near the point $\mathfrak{x}$ of the complex manifold $X$, equipped with a factorization $f = f_{1} \cdots f_{r}$, we consider the $\mathscr{D}_{X,\mathfrak{x}}[s_{1}, \dots, s_{r}]$-module generated by $ F^{S} := f_{1}^{s_{1
Externí odkaz:
http://arxiv.org/abs/1907.05301