共查询到20条相似文献,搜索用时 31 毫秒
1.
《Journal of Pure and Applied Algebra》2022,226(7):106987
We study the relation between zero loci of Bernstein-Sato ideals and roots of b-functions and obtain a criterion to guarantee that roots of b-functions of a reducible polynomial are determined by the zero locus of the associated Bernstein-Sato ideal. Applying the criterion together with a result of Maisonobe we prove that the set of roots of the b-function of a free hyperplane arrangement is determined by its intersection lattice.We also study the zero loci of Bernstein-Sato ideals and the associated relative characteristic cycles for arbitrary central hyperplane arrangements. We prove the multivariable conjecture of Budur for complete factorizations of arbitrary hyperplane arrangements, which in turn proves the strong monodromy conjecture for the associated multivariable topological zeta functions. 相似文献
2.
The Monodromy Conjecture asserts that if c is a pole of the local topological zeta function of a hypersurface, then exp(2πic) is an eigenvalue of the monodromy on the cohomology of the Milnor fiber. A stronger version of the conjecture asserts that
every such c is a root of the Bernstein-Sato polynomial of the hypersurface. In this note we prove the weak version of the conjecture
for hyperplane arrangements. Furthermore, we reduce the strong version to the following conjecture: −n/d is always a root of the Bernstein-Sato polynomial of an indecomposable essential central hyperplane arrangement of d hyperplanes in C
n
. 相似文献
3.
Pratyoosh Kumar 《Journal of Functional Analysis》2010,258(7):2453-2482
We shall obtain inequalities for Fourier transform via moduli of continuity on NA groups. These results in particular settle the conjecture posed in a recent paper by W.O. Bray and M. Pinsky in the context of noncompact rank one symmetric spaces. These problems naturally demand versions of Fourier restriction theorem on these spaces which we shall prove. We shall also elaborate on the connection between the restriction theorem and the Kunze-Stein phenomena on NA groups. For noncompact Riemannian symmetric spaces of rank one analogues of all the results follow the same way. 相似文献
4.
Koichi Kaizuka 《Journal of Functional Analysis》2019,276(2):329-379
In this paper we develop the scattering theory for the Laplacian on symmetric spaces of noncompact type. We study the asymptotic properties of the resolvent in the framework of the Agmon–Hörmander space. Our approach is based on a detailed analysis of the Helgason Fourier transform and generalized spherical functions on symmetric spaces of noncompact type. As an application of our scattering theory, we prove a conjecture by Strichartz concerning a characterization of a family of generalized eigenfunctions of the Laplacian. 相似文献
5.
We use algebraic topology to investigate local curvature properties of the moduli spaces of gauged vortices on a closed Riemann surface. After computing the homotopy type of the universal cover of the moduli spaces (which are symmetric products of the surface), we prove that, for genus $g>1$ , the holomorphic bisectional curvature of the vortex metrics cannot always be nonnegative in the multivortex case, and this property extends to all Kähler metrics on certain symmetric products. Our result rules out an established and natural conjecture on the geometry of the moduli spaces. 相似文献
6.
We study Duflo's conjecture on the isomorphism between
the center of the algebra of invariant differential
operators on a homogeneous space and the center of the
associated Poisson algebra. For a rather wide class of
Riemannian homogeneous spaces, which includes the class
of (weakly) commutative spaces, we prove the "weakened
version" of this conjecture. Namely, we prove that
some localizations of the corresponding centers are
isomorphic. For Riemannian homogeneous spaces of the
form X = (H ⋌ N)/H, where N is a
Heisenberg group, we prove Duflo's conjecture in its
original form, i.e., without any localization. 相似文献
7.
Robert F. Bailey 《Discrete Mathematics》2009,309(13):4253-4265
We replace the usual setting for error-correcting codes (i.e. vector spaces over finite fields) with that of permutation groups. We give an algorithm which uses a combinatorial structure which we call an uncovering-by-bases, related to covering designs, and construct some examples of these. We also analyse the complexity of the algorithm.We then formulate a conjecture about uncoverings-by-bases, for which we give some supporting evidence and prove for some special cases. In particular, we consider the case of the symmetric group in its action on 2-subsets, where we make use of the theory of graph decompositions. Finally, we discuss the implications this conjecture has for the complexity of the decoding algorithm. 相似文献
8.
Tobias Berger 《manuscripta mathematica》2008,125(4):427-470
We study the arithmetic of Eisenstein cohomology classes for symmetric spaces associated to GL2 over imaginary quadratic fields. We prove in many cases a lower bound on their denominator in terms of an L-value of a Hecke character providing evidence for a conjecture of Harder that the denominator is given by this L-value. Furthermore, we exibit conditions under which the restriction of the classes to the boundary is integral. 相似文献
9.
Luke Oeding 《Journal of Pure and Applied Algebra》2011,215(6):1516-1527
We prove a set-theoretic version of the Landsberg-Weyman Conjecture on the defining equations of the tangential variety of a Segre product of projective spaces. We introduce and study the concept of exclusive rank. For the proof of this conjecture, we use a connection to the author’s previous work and re-express the tangential variety as the variety of principal minors of symmetric matrices that have exclusive rank no more than 1. We discuss applications to semiseparable matrices, tensor rank versus border rank, context-specific independence models and factor analysis models. 相似文献
10.
Adrian D. Banner 《Geometriae Dedicata》2001,88(1-3):113-133
M. Cowling, A. H. Dooley, A. Korányi and F. Ricci used groups of Heisenberg type in order to study the symmetric spaces of rank one of noncompact type in a unified manner. This paper extends this work by using the same formulation to investigate the boundaries of these spaces. In particular, we prove a conjecture of Korányi concerning metrics on the boundary and demonstrate that the classical Cayley transform extends to a 1-quasiconformal map of the boundary. 相似文献
11.
Boris Goldfarb 《Topology and its Applications》2004,140(2-3):267-294
New compactifications of symmetric spaces of noncompact type X are constructed using the asymptotic geometry of the Borel–Serre enlargement. The controlled K-theory associated to these compactifications is used to prove the integral Novikov conjecture for arithmetic groups. 相似文献
12.
We prove lower bounds for the entropy of limit measures associated to non-degenerate sequences of eigenfunctions on locally symmetric spaces of non-positive curvature. In the case of certain compact quotients of the space of positive definite n × n matrices (any quotient for n = 3, quotients associated to inner forms in general), measure classification results then show that the limit measures must have a Haar component. This is consistent with the conjecture that the limit measures are absolutely continuous. 相似文献
13.
《中国科学 数学(英文版)》2017,(4)
We conjecture a formula for the generating function of genus one Gromov-Witten invariants of the local Calabi-Yau manifolds which are the total spaces of splitting bundles over projective spaces. We prove this conjecture in several special cases, and assuming the validity of our conjecture we check the integrality of genus one Bogomol'nyi-Prasad-Sommerfield(BPS) numbers of local Calabi-Yau 5-folds defined by Klemm and Pandharipande. 相似文献
14.
XiaoWen Hu 《中国科学 数学(英文版)》2017,60(4):613-636
We conjecture a formula for the generating function of genus one Gromov-Witten invariants of the local Calabi-Yau manifolds which are the total spaces of splitting bundles over projective spaces. We prove this conjecture in several special cases, and assuming the validity of our conjecture we check the integrality of genus one Bogomol’nyi-Prasad-Sommerfield (BPS) numbers of local Calabi-Yau 5-folds defined by Klemm and Pandharipande. 相似文献
15.
We consider symmetry properties of solutions to nonlinear elliptic boundary value problems defined on bounded symmetric domains
of
\mathbb Rn{\mathbb R^n} . The solutions take values in ordered Banach spaces E, e.g.
E=\mathbb RN{E=\mathbb R^N} ordered by a suitable cone. The nonlinearity is supposed to be quasimonotone increasing. By considering cones that are different
from the standard cone of componentwise nonnegative elements we can prove symmetry of solutions to nonlinear elliptic systems
which are not covered by previous results. We use the method of moving planes suitably adapted to cover the case of solutions
of nonlinear elliptic problems with values in ordered Banach spaces. 相似文献
16.
《Journal of Pure and Applied Algebra》2024,228(2):107471
We prove Steinebrunner's conjecture on the biequivalence between (coloured) properads and labelled cospan categories. The main part of the work is to establish a 1-categorical, strict version of the conjecture, showing that the category of properads is equivalent to a category of strict labelled cospan categories via the symmetric monoidal envelope functor. 相似文献
17.
We study linearly ordered spaces which are Valdivia compact in their order topology. We find an internal characterization of these spaces and we present a counter-example disproving a conjecture posed earlier by the first author. The conjecture asserted that a compact line is Valdivia compact if its weight does not exceed ℵ1, every point of uncountable character is isolated from one side and every closed first countable subspace is metrizable. It turns out that the last condition is not sufficient. On the other hand, we show that the conjecture is valid if the closure of the set of points of uncountable character is scattered. This improves an earlier result of the first author. 相似文献
18.
Vladimir L. Shchur 《Functional Analysis and Other Mathematics》2010,3(1):97-101
We generalize and prove a conjecture by V.I. Arnold on the parity of Frobenius numbers. For the case of symmetric semigroups
with three generators we give an exact formula for Frobenius numbers, which is, in a sense, a sum of two Sylvester’s formulae.
We prove that a fraction of symmetric semigroups vanishes in the weak limit. 相似文献
19.
20.
We prove a conjecture of Cuttler et al. (2011) on the monotonicity of normalized Schur functions under the usual (dominance) partial-order on partitions. We believe that our proof technique may be helpful in obtaining similar inequalities for other symmetric functions. 相似文献