Related papers: Successive vanishing on curves
Dimension-varying linear systems are investigated. First, a dimension-free state space is proposed. A cross dimensional distance is constructed to glue vectors of different dimensions together to form a cross-dimensional topological space.…
We prove the vanishing of certain low degree cohomologies of some induced representations. As an application, we determine certain low degree cohomologies of congruence groups.
A new generalization of the classical separate algebraicity theorem is suggested and proved.
Approximate vanishing ideal is a concept from computer algebra that studies the algebraic varieties behind perturbed data points. To capture the nonlinear structure of perturbed points, the introduction of approximation to exact vanishing…
We formulate and establish a generalization of Koll\'ar's injectivity theorem for adjoint bundles twisted by suitable multiplier ideal sheaves. As applications, we generalize Koll\'ar's torsion-freeness, Koll\'ar's vanishing theorem, and a…
We consider a certain linear recursive relation with integer parameters and study some of its algebraic and geometric properties, with the purpose of estimating the number of chains of valences in the Farey series.
In this work, we prove the vanishing of the two cohomological group of the higher local field. This generalize the well-known propriety of finite field and one dimensional local field. We apply this result to study the arithmetic of curve…
Using the relations between rational functions and Eisenstein series, as well as the inferences for cotangent sums and period polynomials, we work out a precise description for Eisenstein series whose $L$-series vanish at certain critical…
We show that every thick subcategory of the singularity category of a complete intersection ring is self dual. We also prove the analogous statement for thick subcategories of the bounded derived category and give applications to the…
In this paper, we study the exact multiplicity and bifurcation curves of positive solutions for the semipositone problem defined on the interval from minus one to one, with zero boundary conditions at both ends. The function f is twice…
This paper is devoted to the study of some connections between coadjoint orbits in infinite dimensional Lie algebras, isospectral deformations and linearization of dynamical systems. We explain how results from deformation theory,…
We give a theorem on the effective non-vanishing problem for algebraic surfaces in positive characteristic. For the Kawamata-Viehweg vanishing, the logarithmic Kollar vanishing and the logarithmic semipositivity, we give their…
We prove an injectivity theorem for the cohomology of the Du Bois complexes of varieties with isolated singularities. We use this to deduce vanishing statements for the cohomologies of higher Du Bois complexes of such varieties. Besides…
We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…
We consider the problem of solving a linear system of equations which involves complex variables and their conjugates. We characterize when it reduces to a complex linear system, that is, a system involving only complex variables (and not…
Using the vanishing cycles of simple singularities, we study the eigenvectors of Cartan matrices of finite root systems, and of q-deformations of these matrices.
In this paper, we use the perspective of linear series, and in particular results following from the degeneration tools of limit linear series, to give a number of new results on existence and non-existence of branched covers of the…
A formula for the irregularity of a cyclic multiple plane associated to a branch curve that has arbitrary singularities and is transverse to the line at infinity is established. The irregularity is expressed as a sum of superabundances of…
Some linear dynamical systems over finite fields are studied and the self-similar character of their development is proved. Connections with aperiodic tilings, Delanoy numbers and other topics are also proved. The prime fields F_p have a…
Parametric models in vector spaces are shown to possess an associated linear map. This linear operator leads directly to reproducing kernel Hilbert spaces and affine- / linear- representations in terms of tensor products. From the…