Related papers: Holomorphic line bundles on a special abelian surf…

We prove that the nonvarying strata of abelian and quadratic differentials in [CM1, CM2] have trivial tautological rings and are affine varieties. We also prove that strata of $k$-differentials of infinite area are affine varieties for all…

We give a natural parameterization of the N\'eron-Severi group of a product $A = E\times E'$ of two elliptic curves in terms of quadratic forms. As an application, we determine (in the non-CM case) whether $A$ contains a smooth curve of any…

We construct nontrivial homomorphisms from the quasi group of some cubic surfaces over $\bbF_{\!p}$ into a group. We show experimentally that the homomorphisms constructed are the only possible ones and that there are no nontrivial…

Motivated by the physical concept of special geometry two mathematical constructions are studied, which relate real hypersurfaces to tube domains and complex Lagrangean cones respectively. Me\-thods are developed for the classification of…

We consider the moduli space of vector bundles of rank $n$ and degree $ng$ over a fixed Riemann surface of genus $g\geq 2$. We use the explicit parametrization in terms of the Tyurin data. In the moduli space there is a "non-abelian" Theta…

The present work deals with the canonical map of smooth, compact complex surfaces of general type in a polarization of type $(1,2,2)$ on an abelian threefold. A natural and classical question is whether the canonical system of such surfaces…

A three-dimensional orbifold $(\Sigma, \gamma_i, n_i)$, where $\Sigma$ is a rational homology sphere, has a universal abelian orbifold covering, whose covering group is the first orbifold homology. A singular pair $(X,C)$, where $X$ is a…

The study of the moduli of covers of the projective line leads to the theory of Hurwitz varieties covering configuration varieties. Certain one-dimensional slices of these coverings are particularly interesting Belyi maps. We present…

Inspired by Bondal's conjecture, we study the behavior of exceptional sequences of line bundles on rational C*-surfaces under homogeneous degenerations. In particular, we provide a sufficient criterion for such a sequence to remain…

We study the classification of affine holomorphic bundles over a compact complex manifold $X$ in general, and we apply the general theory to the case $X=\mathbb{P}^1_\mathbb{C}$. We study the moduli space of framed, non-degenerate rank 2…

Any leafwise connection on a fibre bundle over a foliated manifold is proved to come from a connection on this fibre bundle.

It is in general unknown which topological complex vector bundles on a non-algebraic surface admit holomorphic structures. We solve this problem for primary Kodaira surfaces by using results of Kani on curves of genus two with elliptic…

We study the equations of abelian surfaces embedded in P^{n-1} with a line bundle of polarization of type (1,n). For n>9, we show that the ideal of a general abelian surface with this polarization is generated by quadrics, and if the…

We investigate orthogonal and symplectic bundles with parabolic structure, over a curve.

In this paper we consider the stratification on the moduli space of principally polarized abelian surfaces in characteristic $p>0$ defined by the height of the formal group associated to $H^2(X,O_X)$. We compute the cycle classes of the…

Let $X$ be a toric Del-Pezzo surface and let $Crit(W) \subset (\mathbb{C}^{\ast})^n$ be the solution scheme of the Landau-Ginzburg system of equations. Denote by $X^{\circ}$ the polar variety of $X$. Our aim in this work is to describe a…

We construct infinitely many non-isotrivial families of abelian varieties over given four punctured projective lines. These families lead to algebraic solutions of Painleve VI equation. Finally, based on a recent paper by Lin-Sheng-Wang, we…

We investigate the existence, and lack of unicity, of a holomorphic fibration by discs transversal to a rational curve in a complex surface.

Let A be a finite abelian group. We set up an algebraic framework for studying A-equivariant complex-orientable cohomology theories in terms of a suitable kind of equivariant formal groups. We compute the equivariant cohomology of many…

Given a holomorphic conic bundle without sections, we show that finite groups acting by its fiberwise bimeromorphic transformations are bounded. This provides an analog of a similar result obtained by T.Bandman and Yu.Zarhin for…