Related papers: Trigonal curves and Galois Spin(8)-bundles

We study the derived category of the moduli space $SU_C(2)$ of rank $2$ vector bundles on a smooth projective curve $C$ of genus $g\ge 2$ with trivial determinant. This generalizes the recent work by Tevelev and Torres on the case with…

We explore some of the interplay between Brill-Noether subvarieties of the moduli space SU_C(2,K) of rank 2 bundles with canonical determinant on a smooth projective curve and 2\theta divisors, via the inclusion of the moduli space into…

Let SU_X(3) be the moduli space of semi-stable vector bundles of rank 3 and trivial determinant on a curve X of genus 2. It maps onto P^8 and the map is a double cover branched over a sextic hypersurface called the Coble sextic. In the dual…

Let $C$ be a curve of genus two. We denote by $SU_C(3)$ the moduli space of semi-stable vector bundles of rank 3 and trivial determinant over $C$, and by $J^d$ the variety of line bundles of degree $d$ on $C$. In particular, $J^1$ has a…

Let SU_C(2) be the moduli space of rank 2 semistable vector bundles with trivial de terminant on a smooth complex algebraic curve C of genus g > 1, we assume C non-hyperellptic if g > 2. In this paper we construct large families of pointed…

Let $C$ be a curve with two smooth components and a single node. Let $\mathcal{U}_C(r,w,\chi)$ be the moduli space of $w$-semistable classes of depth one sheaves on $C$ having rank $r$ on both components and Euler characteristic $\chi$. In…

Given a smooth genus three curve $C$, the moduli space of rank two stable vector bundles on C with trivial determinant embeds in $\mathbb{P}^8$ as a hypersurface whose singular locus is the Kummer threefold of $C$; this hypersurface is the…

According to Mukai, any prime Fano threefold X of genus 7 is a linear section of the spinor tenfold in the projectivized half-spinor space of Spin(10). It is proven that the moduli space of stable rank-2 vector bundles with Chern classes…

Our aim is to determine the tautological algebra generated by the cohomology classes of the Brill-Noether loci in the rational cohomology of the moduli stack $\mathcal{U}_C(n,d)$ of semistable bundles of rank $n$ and degree $d$. We show…

Let $C$ be an elliptic curve, $w\in C$, and let $S\subset C$ be a finite subset of cardinality at least $3$. We prove a Torelli type theorem for the moduli space of rank two parabolic vector bundles with determinant line bundle $\mathcal…

Let X be a smooth projective curve of genus g \geq 2 defined over a field of characteristic two. We give examples of stable orthogonal bundles with unstable underlying vector bundles and use them to give counterexamples to Behrend's…

We prove the existence of a projective good moduli space of principal $\mathcal{G}$-bundles under nonconnected reductive group schemes $\mathcal{G}$ over a smooth projective curve $C$. We also prove that the moduli stack of…

Let $C$ be an algebraic smooth complex genus $g>1$ curve. The object of this paper is the study of the birational structure of the coarse moduli space $U_C(r,0)$ of semi-stable rank r vector bundles on $C$ with degree 0 determinant and of…

The aim of this paper is two--fold. We first strongly improve our previous main result Theorem 3.1 in Arxiv 1702.00918v3 12Feb2018 ("Brill-Noether loci of rank two vector bundles on a general $\nu$-gonal curve"), concerning classification…

Let N be the moduli space of stable rank 2 quasiparabolic vector bundles of fixed degree on the projective line with 2g+1 marked points, where g>1, and stability is with respect to the weights {0,1/2} at each marked point. In this note we…

Given any irreducible smooth complex projective curve $X$, of genus at least $2$, consider the moduli stack of vector bundles on $X$ of fixed rank and determinant. It is proved that the isomorphism class of the stack uniquely determines the…

We study rank-2 wobbly bundles on a Riemann surface $C$ of genus $g\geq 2$, i.e. semi-stable bundles admitting nonzero nilpotent Higgs fields, in terms of direct images of line bundles on smooth spectral curves $\tilde{C}…

Let $C$ be a smooth irreducible complex projective curve of genus $g$ and let $B^k(2,K_C)$ be the Brill-Noether loci parametrizing classes of (semi)-stable vector bundles $E$ of rank two with canonical determinant over $C$ with…

We examine a moduli problem for real and quaternionic vector bundles on a smooth complex projective curve with a fixed real structure, and we give a gauge-theoretic construction of moduli spaces for semi-stable such bundles with fixed…

For a smooth projective curve $X$ over $\mathbb C_p$ and any reductive group $G$, we show that the moduli stack of $G$-Higgs bundles on $X$ is a twist of the moduli stack of v-topological $G$-bundles on $X_v$ in a canonical way. We explain…