Related papers: Quadric bundles and their moduli spaces

Classification theory and the study of projective varieties which are covered by rational curves of minimal degrees naturally leads to the study of families of singular rational curves. Since families of arbitrarily singular curves are hard…

Any oriented 4-dimensional real vector bundle is naturally a line bundle over a bundle of quaternion algebras. In this paper we give an account of modules over bundles of quaternion algebras, discussing Morita equivalence, characteristic…

In this paper we provide two ways of constructing complex coordinates on the moduli space of pairs of a Riemann surface and a stable holomorphic vector bundle centred around any such pair. We compute the transformation between the…

In this paper, we study the moduli space of Higgs pairs, which can be considered as a generalization of holomorphic pairs. Higgs pairs are an example of quiver bundles. We introduce the notion of $\tau$-stability of Higgs pairs for…

We show the existence of a symplectic structure on the moduli space of the Seiberg-Witten equations on $\Sigma \times \Sigma$ where $\Sigma$ is a compact oriented Riemann surface. To prequantize the moduli space, we construct a Quillen-type…

We prove that the modular component $\mathcal M(r)$, constructed in the Main Theorem of a former paper of us (published in Adv. Math on 2024), paramatrizing (isomorphism classes of) Ulrich vector bundles of rank $r$ and given Chern classes,…

We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…

This paper concerns the moduli spaces of rank two parabolic Higgs bundles and parabolic K(D) pairs over a smooth curve. Precisely which parabolic bundles occur in stable K(D), pairs and stable Higgs bundles is determined. Using Morse…

In this paper we continue our study of the moduli space of stable bundles of rank two and degree 1 on a very general quintic surface. The goal in this paper is to understand the irreducible components of the moduli space in the first case…

We classify the connected components of the space of representations of the fundamental group of a closed oriented surface of genus $\geq 2$ in $Sp(4,{\mathbf R})$. We prove that this is equivalent to classifying the connected components of…

We give an algebro-geometric derivation of the known intersection theory on the moduli space of stable rank 2 bundles of odd degree over a smooth curve of genus g. We lift the computation from the moduli space to a Quot scheme, where we…

In this paper, we compare the moduli spaces of rank-3 vector bundles stable with respect to different ample divisors over rational ruled surfaces. We also discuss the irreducibility, unirationality, and rationality of these moduli spaces.

Fix a ruled surface S obtained as the projective completion of a line bundle L on a complex elliptic curve; we study the moduli problem of parametrizing certain pairs consisting of a sheaf E on S and a map of E to a fixed reference sheaf on…

Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…

We construct new stable vector bundles on Hilbert schemes of points on algebraic surfaces, which are parametrised by connected components of their moduli spaces. This work generalises aspects of our previous work on tautological bundles and…

By means of a Fourier-Mukai transform we embed moduli spaces of stable bundles on an algebraic curve C as isotropic subvarieties of moduli spaces of mu-stable bundles on the Jacobian variety J(C). When g(C)=2 this provides new examples of…

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 Desale-Ramanan Theorem is an isomorphism between the moduli space of rank two vector bundles over complex hyperelliptic curve and the variety of linear subspaces in an intersection of two quadrics. We prove a real version of this…

In this paper we continue our study on the moduli spaces of flat G-bundles, for any semi-simple Lie group G, over a Riemann surface by using heat kernel and Reidemeister torsion. Formulas for intersection numbers on the moduli spaces over a…

We quantize the coordinate ring of the moduli space of B-bundles on the elliptic curve. Here B is a Borel subgroup of some semisimple Lie group. We construct some representations of these algebras and study intertwining operators for these…