Related papers: Note on the Ruijsenaars-Schneider model

A plane curve C defined by a homogeneous polynomial satisfying Laplace's equation appears canonically as the vanishing of the Pfaffian of a skew-symmetric matrix of linear forms. As a consequence there is a natural semi-stable rank two…

Drawing on work of Berndtsson and of Lempert and Sz\H{o}ke, we define a kind of complex analytic structure for families of (possibly finite-dimensional) Hilbert spaces that might not fit together to form a holomorphic vector bundle but…

We compare the behaviour of entire curves and integral sets, in particular in relation to locally trivial fiber bundles, algebraic groups and finite ramified covers over semi-abelian varieties.

We define the notion of C^{(2)}_{N+1} Ruijsenaars-Schneider models and construct their Lax formulation. They are obtained by a particular folding of the A_{2N+1} systems. Their commuting Hamiltonians are linear combinations of…

In this paper, we survey recent developments in the Brill-Noether Theory of higher rank vector bundles on complex projective surfaces. We focus on weak Brill-Noether Theorems on rational and K-trivial surfaces and their applications.

In continuation of our work in Comm. in Algebra, vol. 28 (2000), we study ramified coverings of projective manifolds, in particular over Fano manifolds and investigate positivity properties of the associated vector bundle. Moreover we study…

Let $X$ be any smooth simply connected projective surface. We consider some moduli space of pure sheaves of dimension one on $X$, i.e. $\mhu$ with $u=(0,L,\chi(u)=0)$ and $L$ an effective line bundle on $X$, together with a series of…

Conjecture 9B from the previous version of the paper stating that any holomorphic vector bundle on an elliptic curve can be realized by a scalar differential equation has now been proved by the authors. The proof is included in the new…

We study closures of GL_2(R)-orbits on the total space of the Hodge bundle over the moduli space of curves under the assumption that they are algebraic manifolds. We show that, in the generic stratum, such manifolds are the whole stratum,…

We observe that if we are interested primarily in degeneration arguments, there is a weaker notion of (semi)stability for vector bundles on reducible curves, which is sufficient for many applications, and does not depend on a choice of…

Let W be the germ of a smooth complex surface around an exceptional curve and let E be a rank 2 vector bundle on W. We study the cohomological properties of a finite sequence $E_i, 1 \leq i \leq t$ of rank 2 vector bundles canonically…

We discuss some topological aspects of the Riemann-Hilbert transmission problem and Riemann-Hilbert monodromy problem on Riemann surfaces. In particular, we describe the construction of a holomorphic vector bundle starting from the given…

This paper is the first in a series of three devoted to the smooth classification of simply connected elliptic surfaces. The method is to compute some coefficients of Donaldson polynomials of $SO(3)$ invariants whose second Stiefel-Whitney…

We classify elliptic curves over the rationals whose N\'eron model over the integers is semi-abelian, with good reduction at p=2, and whose Mordell--Weil group contains an element of order two that stays non-trivial at p=2. Furthermore, we…

We study systems involving vector bundles and logarithmic connections on Riemann surfaces and linear algebra data linking their residues. This generalizes representations of deformed preprojective algebras. Our main result is the existence…

We investigate the analog of holomorphic vector bundles in the context of Sasakian manifolds.

We use hypersurfaces containing unexpected linear spaces to construct interesting vector bundles on complete intersection surfaces in projective space. We discover examples of moduli spaces of rank 2 stable bundles on surfaces of Picard…

We present a geometric interpretation of tight closure in terms of vector bundles and projective bundles.

For any (n-1)-dimensional simplicial complex, we construct a particular n-dimensional complex vector bundle over the associated Davis-Januszkiewicz space whose Chern classes are given by the elementary symmetric polynomials in the…

We propose a matrix regularization of vector bundles over a general closed K\"ahler manifold. This matrix regularization is given as a natural generalization of the Berezin-Toeplitz quantization and gives a map from sections of a vector…