Related papers: Algebraic Gromov ellipticity: a brief survey
The classical definition of Prym varieties deals with the unramified covers of curves. The aim of the present paper is to give explicit algebraic descriptions of the Prym varieties associated to ramified double covers of algebraic curves.…
This note provides new closed forms evaluations of a few classes of exponential sums associated with elliptic curves and hyperelliptic curves.
We compute various types of iterated integrals of Eisenstein-Kronecker forms that are constructed from the Kronecker theta function. Furthermore, we relate the generating series of Gromov-Witten invariants of elliptic curves to these…
The paper collects different approaches and viewpoints on bilinear forms and hermitian forms around isolated hypersurface singularities. It gives the relations between them in precise formulas. It does not contain new results.
We find new examples of complex surfaces with countably many non-isomorphic algebraic structures. Here is one such example: take an elliptic curve $E$ in $\mathbb P^2$ and blow up nine general points on $E$. Then the complement $M$ of the…
A priori, the set of birational transformations of an algebraic variety is just a group. We survey the possible algebraic structures that we may add to it, using in particular parametrised family of birational transformations.
In this review we discuss what is known about semiorthogonal decompositions of derived categories of algebraic varieties. We review existing constructions, especially the homological projective duality approach, and discuss some related…
We present the topological classification of real parts of real regular elliptic surfaces with a real section.
We prove a transformation formula relating two determinants involving elliptic shifted factorials. Similar determinants have been applied to multiple elliptic hypergeometric series.
This book is expository and is in Russian. It is shown how in the course of solution of interesting geometric problems (close to applications) naturally appear main notions of algebraic topology (homology groups, obstructions and…
These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.
We compute stationary gravitational descendants in symplectic ellipsoids of any dimension, and use these to derive a number of new recursive formula for punctured curve counts in symplectic manifolds with ellipsoidal ends. Along the way we…
We look for elliptic curves featuring rational points whose coordinates form two arithmetic progressions, one for each coordinate. A constructive method for creating such curves is shown, for lengths up to 5.
This paper surveys recent results on classifying partially hyperbolic diffeomorphisms. This includes the construction of branching foliations and leaf conjugacies on three-dimensional manifolds with solvable fundamental group.…
Several results on presenting an affine algebraic group variety as a product of algebraic varieties are obtained.
Several new identities for elliptic hypergeometric series are proved. Remarkably, some of these are elliptic analogues of identities for basic hypergeometric series that are balanced but not very-well-poised.
We study higher-degree generalizations of symplectic groupoids, referred to as {\em multisymplectic groupoids}. Recalling that Poisson structures may be viewed as infinitesimal counterparts of symplectic groupoids, we describe "higher''…
We try to understand which morphisms of complex analytic spaces come from algebraic geometry. We start with a series of conjectures, and then give some partial solutions.
We define the singular elliptic genus for arbitrary normal surfaces, prove that it is a birational invariant, and show that it generalizes the singular elliptic genus of Borisov and Libgober and the stringy $\chi_y$ genus of Batyrev and…
This is a survey article on symplectically aspherical manifolds. The paper contains a discussion on constructions of symplectically aspherical manifolds, their topological properties and the role of this class in symplectic topology.…