Search results for "Number"
showing 10 items of 3939 documents
On Higgs bundles over Shimura varieties of ball quotient type
2016
We prove the generic exclusion of certain Shimura varieties of unitary and orthogonal types from the Torelli locus. The proof relies on a slope inequality on surface fibration due to G. Xiao, and the main result implies that certain Shimura varieties only meet the Torelli locus in dimension zero.
Transcendental lattices of some K 3-surfaces
2008
In a previous paper, (S2), we described six families of K3-surfaces with Picard- number 19, and we identified surfaces with Picard-number 20. In these notes we classify some of the surfaces by computing their transcendental lattices. Moreover we show that the surfaces with Picard-number 19 are birational to a Kummer surface which is the quotient of a non-product type abelian surface by an involution.
On a Theorem of Greuel and Steenbrink
2017
A famous theorem of Greuel and Steenbrink states that the first Betti number of the Milnor fibre of a smoothing of a normal surface singularity vanishes. In this paper we prove a general theorem on the first Betti number of a smoothing that implies an analogous result for weakly normal singularities.
Stable Images and Discriminants
2020
We show that the discriminant/image of a stable perturbation of a germ of finite \(\mathcal {A}\)-codimension is a hypersurface with the homotopy type of a wedge of spheres in middle dimension, provided the target dimension does not exceed the source dimension by more than one. The number of spheres in the wedge is called the discriminant Milnor number/image Milnor number. We prove a lemma showing how to calculate this number, and show that when the target dimension does not exceed the source dimension, the discriminant Milnor number and the \(\mathcal {A}\)-codimension obey the “Milnor–Tjurina relation” familiar in the case of isolated hypersurface singularities. This relation remains conj…
Projecting 4-folds from G(1, 5) to G(1, 4)
2002
We study 4-dimensional subvarieties of the Grassmannian G(1,5) with singular locus of dimension at most 1 that can be isomorphically projected to G(1,4).
Equidistribution and Counting of Quadratic Irrational Points in Non-Archimedean Local Fields
2019
We use these results to deduce equidistribution and counting results of quadratic irrational elements in non-Archimedean local fields.
Banach partial *-algebras: an overview
2019
A Banach partial $*$-algebra is a locally convex partial $*$-algebra whose total space is a Banach space. A Banach partial $*$-algebra is said to be of type (B) if it possesses a generating family of multiplier spaces that are also Banach spaces. We describe the basic properties of these objects and display a number of examples, namely, $L^p$-like function spaces and spaces of operators on Hilbert scales or lattices. Finally we analyze the important cases of Banach quasi $*$-algebras and $CQ^*$-algebras.
"Fixed Point Theorems for '?, ?'Contractive maps in Weak nonArchimedean Fuzzy Metric Spaces and Application"
2011
The present study introduce the notion of (ψ, ϕ)-Contractive maps in weak non-Archimedean fuzzy metric spaces to derive a common fixed point theorem which complements and extends the main theorems of [C.Vetro, Fixed points in weak non-Archimedean fuzzy metric spaces, Fuzzy Sets and System, 162 (2011), 84-90] and [D.Mihet, Fuzzy ψ-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets and System, 159 (2008) 739-744]. We support our result by establishing an application to product spaces.
Principal Values of Cauchy Integrals, Rectifiable Measures and Sets
1991
The extensive studies started by A. P. Calderon in the sixties and continued by many authors up today have revealed that the Cauchy integrals $$ {C_{\Gamma }}f(z) = \int_{\Gamma } {\frac{{f\left( \zeta \right)d\zeta }}{{\zeta - z}}} $$ behave very well on sufficiently regular, not necessarily smooth, curves F, see [CCFJR], [D] and [MT].
Decomposition numbers and local properties
2020
Abstract If G is a finite group and p is a prime, we give evidence that the p-decomposition matrix encodes properties of p-Sylow normalizers.