Related papers: Holomorphic 1-forms on the moduli space of curves

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…

The space $\mathbf{H}^{4,2}$ of vectors of norm -1 in $\mathbb{R}^{4,3}$ has a natural pseudo-Riemannian metric and a compatible almost complex structure. The group of automorphisms of both of these structures is the split real form $G_2'$.…

Let G be a reductive group over an algebraically closed field of positive characteristic. Let C be a smooth projective curve over k. We give a description of the moduli space of flat G-bundles in terms of the moduli space of G-Higgs bundles…

Let ${\mathcal M}$ be a moduli space of stable vector bundles of rank $r$ and determinant $\xi$ on a compact Riemann surface $X$. Fix a semistable holomorphic vector bundle $F$ on $X$ such that $\chi(E\otimes F)= 0$ for $E \in \mathcal M$.…

We describe the first order moduli space of heterotic string theory compactifications which preserve $N=1$ supersymmetry in four dimensions, that is, the infinitesimal parameter space of the Strominger system. We establish that if we…

We construct a new compactification of the moduli space of maps from pointed nonsingular projective stable curves to a nonsingular projective variety with prescribed ramification indices at the points. It is shown to be a proper…

Let $G$ be a simple and simply connected complex Lie group. We discuss the moduli space of holomorphic semistable principal $G$ bundles over an elliptic curve $E$. In particular we give a new proof of a theorem of Looijenga and…

We prove that moduli spaces of torsion-free sheaves on a projective smooth complex surface are irreducible, reduced and of the expected dimension, provided the expected dimension is large enough. Actually we prove more: given a line bundle…

In this article, we investigate Hecke modifications of vector bundles on a smooth projective curve $X$ defined over an arbitrary field. We obtain structural results that allow us to reduce the classification problem of Hecke modifications…

For an arbitrary reductive group $G$, we compute the infinitesimal automorphisms of $L$-valued principal $G$-Higgs bundles over a compact K\"ahler manifold $X$, extending known results for $\Omega_X^{1}$-valued $G$-Higgs bundles. Using this…

Let $H$ be a semisimple algebraic group. We prove the semistable reduction theorem for $\mu$--semistable principal $H$--bundles over a {\it smooth projective variety $X$} defined over the field $\bc$. When $X$ is a {\it smooth projective…

Full level-n structures on smooth, complex curves are trivializations of the n-torsion points of their Jacobians. We give an algebraic proof that the etale cohomology of the moduli space of smooth, complex curves of genus at least 2 with…

Let X be a smooth projective variety over the complex numbers, and let D be an ample divisor in X. For which spaces Y is the restriction map r: Hom(X, Y) -> Hom(D, Y) an isomorphism? Using positive characteristic methods, we give a fairly…

We describe the moduli space G^r_d of triples consisting of a curve C, a line bundle L on C of degree d, and a linear system V on L of dimension r. This moduli space extends over a partial compactification {\tilde M_g} of M_g inside {\bar…

In the last years the biregular automorphisms of the Deligne-Mumford's and Hassett's compactifications of the moduli space of n-pointed genus g smooth curves have been extensively studied by A. Bruno and the authors. In this paper we give a…

There is a canonical isomorphism between the coarse moduli spaces of somooth hyperelliptic curves of genus g and binary forms of degree 2g+2 with nonzero discriminant. In this paper, we study the extension of this isomorphism to the…

We show that the moduli space of degree $e$ maps from smooth genus $g \ge 1$ curves to an arbitrary low degree smooth hypersurface is singular when $e$ is large compared to $g$. We also give a lower bound for the dimension of the singular…

Let $\overline{\mathcal{M}}_{g,A[n]}$ be the Hassett moduli stack of weighted stable curves, and let $\overline{M}_{g,A[n]}$ be its coarse moduli space. These are compactifications of $\mathcal{M}_{g,n}$ and $M_{g,n}$ respectively, obtained…

We show that the moduli space $M$ of holomorphic vector bundles on $CP^3$ that are trivial along a line is isomorphic (as a complex manifold) to a subvariety in the moduli of rational curves of the twistor space of the moduli space of…

We study the moduli space M(G,A) of flat G-bundles on an Abelian surface A, where G is a compact, simple, simply connected, connected Lie group. Equivalently, M(G,A) is the (coarse) moduli space of s-equivalence classes of holomorphic…