相关论文: Second order theta divisors on Pryms

For $r\geq 3$ and $g= \frac{r(r+1)}{2}$, we study the Prym-Brill-Noether variety $V^r(C,\eta)$ associated to Prym curves $[C,\eta]$. The locus $\mathcal{R}_g^r$ in $\mathcal{R}_g$ parametrizing Prym curves $(C, \eta)$ with nonempty…

We first present a Priestley-style dualitiy for the classes of algebras that are the algebraic counterpart of some congruential, finitary and filter-distributive logic with theorems. Then we analyze which properties of the dual spaces…

A new approach to the algebraic classification of second order symmetric tensors in 5-dimensional space-times is presented. The possible Segre types for a symmetric two-tensor are found. A set of canonical forms for each Segre type is…

This is a slightly expanded version of the talk given by Ch.O. at the conference "Instantons in complex geometry", at the Steklov Institute in Moscow. The purpose of this talk was to explain the algebraic results of our paper "Abelian…

We make a very detailed analysis of the numerical properties of effective divisors whose support is contained in the exceptional locus of a birational morphism of smooth projective surfaces. As an application we extend Miyaoka's inequality…

Del Pezzo surfaces over C with log terminal singularities of index \le 2 were classified by Alekseev and Nikulin. In this paper, for each of these surfaces, we find an appropriate morphism to projective space. These morphisms enable us to…

We study the degenerations of intermediate Jacobians by means of log geometry. We extend the family of intermediate Jacobians over a punctured disc to a "log intermediate Jacobian" over a disc.

Let $X$ be an abelian variety defined over an algebraically closed field $k$. We consider theta groups associated to \emph{simple semi-homogenous vector bundles of separable type} on $X$. We determine the structure and representation theory…

A new proof for adjoint systems of linear equations is presented. The argument is built on the principles of Algorithmic Differentiation. Application to scalar multiplication sets the base line. Generalization yields adjoint inner vector,…

The Riccati equation method is used to establish three new oscillatory criteria for the second order linear ordinary differential equations in the marginal, sub extremal and extremal cases.We show that the first of these criteria implies…

Consider a linear ordering equipped with a finite sequence of monadic predicates. If the ordering contains an interval of order type \omega or -\omega, and the monadic second-order theory of the combined structure is decidable, there exists…

This paper addresses an investigation on a factorization method for difference equations. It is proved that some classes of second order linear difference operators, acting in Hilbert spaces, can be factorized using a pair of mutually…

The Coble cubics were discovered more than a century ago in connection with genus two Riemann surfaces and theta functions. They have attracted renewed interest ever since. Recently, they were reinterpreted in terms of alternating…

In this paper we consider the singularities of the varieties parameterizing stable vector bundles of fixed rank and degree with sections on a smooth curve of genus at least two. In particular, we extend results of Y. Laszlo, and of the…

We describe the isotypical decomposition of the Jacobian variety JW of the Galois extension W-->T of any fourfold cover of smooth connected irreducible projective complex curves X-->T, in terms of Prym's of intermediate covers. We also…

In this text we prove that if an abelian variety $A$ admits an embedding into the Jacobian of a smooth projective curve $C$, and if we consider $\Theta_A$ to be the divisor $\Theta_C\cap A$, where $\Theta_C$ denotes the theta divisor of…

Osculating spaces of decomposable scrolls (of any genus and not necessarily normal)are studied and their inflectional loci are related to those of their generating curves by using systematically an idea introduced by Piene and Sacchiero in…

It is known by results of Koll\'ar, Ein, Lazarsfeld, Hacon and Debarre that divisors representing principal and other low degree polarizations on abelian varieties have mild singularities. In this note we extend such results to…

A theta divisor on the universal principally polarised abelian variety can be extended to a compactification either by taking the Zariski closure, or by taking the unique extension which is pure of weight 2. For the latter, following ideas…

We extend Latimer and MacDuffee's theorem to a general commutative domain and apply this result to study similarity of matrices over integral rings of number fields. We also conjecture similarity over discrete valuation rings can be descent…