Related papers: Successive vanishing on curves
Stratifications and iterative differential equations are analogues in positive characteristic of complex linear differential equations. There are few explicit examples of stratifications. The main goal of this paper is to construct…
The coupled Kadomtsev--Petviashvili system associated with an elliptic curve, proposed by Date, Jimbo and Miwa [J. Phys. Soc. Jpn., 52:766--771, 1983], is reinvestigated within the direct linearisation framework, which provides us with more…
Using linear projections one gets new inequalities for the successive minima of the lattice of sections of an hermitian line bundle on an arithmetic surface.
The purpose of this paper is to give two supplements for vanishing theorems: One is a relative version of the Kawamata-Viehweg-Nadel type vanishing theorem, which is obtained from an observation for the variation of the numerical dimension…
Let L be a linear difference operator with polynomial coefficients. We consider singularities of L that correspond to roots of the trailing (resp. leading) coefficient of L. We prove that one can effectively construct a left multiple with…
We study the vanishing of Massey products of order at least $3$ for absolutely irreducible smooth projective curves over a perfect field with coefficients in $\mathbb{Z}/\ell$. We mainly focus on elliptic curves, for which we obtain a…
In this survey, we report on progress concerning families of projective curves with fixed number and fixed (topological or analytic) types of singularities. We are, in particular, interested in numerical, universal and asymptotically proper…
In the present paper, we establish a general Kawamata-Viehweg-Koll\'ar-Nadel type vanishing theorem for higher direct images in terms of numerical dimension for closed positive currents on compact K\"ahler manifolds, unifying a number of…
A cohomological vanishing property is proved for finitely supported ideals in an arbitrary d-dimensional regular local ring. (Such vanishing implies some refined Briancon-Skoda-type results, not otherwise known in mixed characteristic.) It…
We give a diagrammatic summary of the connections between various theorems and conjectures about the vanishing of the Euler characteristic.
Inside the symmetric product of a very general curve, we consider the codimension-one subvarieties of symmetric tuples of points imposing exceptional secant conditions on linear series on the curve of fixed degree and dimension. We compute…
In this paper, we study the adjoint foliated structures of the form $K_{\mathcal{F}}+D$ on algebraic surfaces, with particular focus on their minimal and canonical models. We investigate the effective behavior of the multiple linear system…
We study an interacting system of competing particles on the real line. Two populations of positive and negative particles evolve according to branching Brownian motion. When opposing particles meet, their charges neutralize and the…
This paper introduces the notion of a derived splinter. Roughly speaking, a scheme is a derived splinter if it splits off from the coherent cohomology of any proper cover. Over a field of characteristic 0, this condition characterises…
In this paper we consider an advection-diffusion equation, in one space dimension, whose diffusivity can be negative. Such equations arise in particular in the modeling of vehicular traffic flows or crowds dynamics, where a negative…
In a recent paper, we obtained a WDVV-type relation for real genus 0 Gromov-Witten invariants with conjugate pairs of insertions; it specializes to a complete recursion in the case of odd-dimensional projective spaces. This note provides…
We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…
The zero set of a real polynomial in two variable is a curve in $\mathbb R^2$. For a generic choice of its coefficients this is a non-singular curve, a collection of circles and lines properly embedded in $\mathbb R^2$. What topological…
We prove some strong results on approximation of strongly semistable bundles with vanishing numerical Chern classes by filtrations, whose quotients are line bundles of similar slope. This generalizes some earlier results of…
We study the projective systems in both continuous and discrete settings. These systems are linearizable by construction and thus, obviously, integrable. We show that in the continuous case it is possible to eliminate all variables but one…