Related papers: Prym varieties and their moduli

We show that certain abelian varieties over $\Q$ with bad reduction at one prime only are modular by using methods based on the tables of Odlyzko and class field theory.

We discuss for an affine variety $Y$ embedded in affine space $X$ two sets of integers attached to $Y\subseteq X$ via local and de Rham cohomology spectral sequences. We give topological interpretations, study them in small dimension, and…

The pentagram map is a discrete integrable system on the moduli space of planar polygons. The corresponding first integrals are so-called monodromy invariants $E_1, O_1, E_2, O_2,\dots$ By analyzing the combinatorics of these invariants,…

This is a slightly revised version of the author's 2010 diploma thesis. It is concerned with the interplay between real multiplication on Jacobian varieties, as the title suggests, and complex geodesics in the moduli space of curves. Large…

In this paper, our aim is to find the relations amongst the cohomology classes of Brill-Noether subvarieties of the moduli space of semistable bundles over an elliptic curve. We obtain results similar to the Poincar\'e relations on a…

We decompose each moduli space of semistable sheaves on the complex projective plane with support of dimension one and degree four into locally closed subvarieties, each subvariety being the good or geometric quotient of a set of morphisms…

In this course we introduce the main notions relative to the classical theory of modular forms. A complete treatise in a similar style can be found in the author's book joint with F. Str{\"o}mberg [1].

This is the authors doctoral thesis written at the Humboldt-University Berlin. It contains material from the three separate papers: "On the Kodaira dimension of the moduli space of nodal curves", "On quotients of…

We study Fourier transforms of regular holonomic D-modules. In particular we show that their solution complexes are monodromic. An application to direct images of some irregular holonomic D-modules will be given. Moreover we give a new…

Let $O_F$ be the ring of integers of a totally real field $F$ of degree $g$. We study the reduction of the moduli space of separably polarized abelian $O_F$-varieties of dimension $g$ modulo $p$ for a fixed prime $p$. The invariants and…

Free Hopf modules and bimodules over a bialgebra are studied with some details. In particular, we investigate a duality in the category of bimodules in this context. This gives the correspondence between Woronowicz's quantum Lie algebra and…

In this note we study the freeness of the module of derivations on all moduli of the $X_3$ arrangement with multiplicities. We use homological techniques stemming from work of Yuzvinsky, Brandt, and Terao which have recently been developed…

We construct natural Riemannian metrics on Seiberg-Witten moduli spaces and study their geometry.

In this paper, we redefine the theory of walls and chambers due to Qin developing a new tool to study moduli spaces of stable rank 2 vector bundles on algebraic varieties of higher dimension. We apply it to describe components of some…

The Geometry of planar domain walls is studied. It is argued that the planar walls indeed have plane symmetry. In the Minkowski coordinates the walls are mapped into revolution paraboloids.

We study the weighted Fock spaces in one and several complex variables. We evaluate the dimension of these spaces in terms of the weight function extending and completing earlier results by Rozenblum-Shirokov and Shigekawa.

We study holomorphic $(n+1)$-chains $E_n\to E_{n-1} \to >... \to E_0$ consisting of holomorphic vector bundles over a compact Riemann surface and homomorphisms between them. A notion of stability depending on $n$ real parameters was…

In this paper, we study several topics on additive decompositions of primitive elemements in finite fields. Also we refine some bounds obtained by Dartyge and S\'{a}rk\"{o}zy and Shparlinski.

This is a survey of recent progress on the irreducibility of Fermi varieties, rigidity results and embedded eigenvalue problems of discrete periodic Schr\"odinger operators.

Given a possibly reducible and non-reduced spectral cover X over a smooth projective complex curve C we determine the group of connected components of the Prym variety Prym(X/C). As an immediate application we show that the finite group of…