Related papers: Projective structures on a Riemann surface

We introduce the notion of level-$\delta$ limit linear series, which describe limits of linear series along families of smooth curves degenerating to a singular curve $X$. We treat here only the simplest case where $X$ is the union of two…

Let X be a geometrically connected smooth projective curve of genus one, defined over the field of real numbers, such that X does not have any real points. We classify the isomorphism classes of all stable real algebraic vector bundles over…

Let $(X,D)$ be an open log del Pezzo surface of rank one, that is, $X$ is a normal projective surface of Picard rank one, the boundary $D$ is a reduced nonzero divisor on $X$, and the anti-log canonical divisor $-(K_X+D)$ is ample. We show…

In this paper we describe a physical realization of a family of non-compact Kahler threefolds with trivial canonical bundle in hybrid Landau-Ginzburg models, motivated by some recent non-Kahler solutions of Strominger systems, and utilizing…

Let $X$ be a complex smooth projective variety of dimension $d$. Under some assumption on the cohomology of $X$, we construct mutually orthogonal idempotents in $CH_d(X \times X) \otimes \Q$ whose action on algebraically trivial cycles…

We show that, for a free abelian group $G$ and prime power $p^\nu$, every direct sum decomposition of the group $G/p^\nu G$ lifts to a direct sum decomposition of $G$. This is the key result we use to show that, if $R$ is a commutative von…

Given a compact Riemann surface $\Sigma$ of genus $g_\Sigma\, \geq\, 2$, and an effective divisor $D\, =\, \sum_i n_i x_i$ on $\Sigma$ with $\text{degree}(D)\, <\, 2(g_\Sigma -1)$, there is a unique cone metric on $\Sigma$ of constant…

Given a complex projective manifold $X$ and a divisor $D$ with normal crossings, we say that the logarithmic tangent bundle $T_X(-\log D)$ is R-flat if its pull-back to the normalization of any rational curve contained in $X$ is the trivial…

Given a measure space ${\mathcal X}$, we can construct a number of induced structures: eg. its $L^2$ space, the space ${\mathcal P}({\mathcal X})$ of probability distributions on ${\mathcal X}$. If, in addition, ${\mathcal X}$ admits a…

We show that a continuously-normed Banach bundle $\mathcal{E}$ over a compact Hausdorff space $X$ whose space of sections is algebraically finitely-generated (f.g.) over $C(X)$ is locally trivial (and hence the section space is projective…

The classical Beauville-Bogomolov Decomposition Theorem asserts that any compact K\"ahler manifold with numerically trivial canonical bundle admits an \'etale cover that decomposes into a product of a torus, and irreducible,…

We study complex solvmanifolds $\Gamma\backslash G$ with holomorphically trivial canonical bundle. We show that the trivializing section of this bundle can be either invariant or non-invariant by the action of $G$. First we characterize the…

A theorem of Wiegerinck asserts that the Bergman space of an open subset of the complex numbers is either infinite-dimensional or trivial. Recently, this has been generalized to holomorphic vector bundles over the projective line by the…

Given a compact Riemann surface $C$, the line in $H^0(J_C,\, 2\Theta)$ orthogonal to the sections vanishing at $0$ produces a natural projective structure on $C$. We investigate the properties of this projective structure.

A long standing conjecture, known to us as the Eisenbud Goto conjecture, states that an n-dimensional variety embedded with degree $d$ in the $N$- dimensional projective space is $(d-(N-n)+1)$-regular in the sense of Castelnuovo-Mumford. In…

For any projective curve $X$ let $\bar{M}^d(X)$ be the Simpson moduli space of pure dimension one rank 1 degree $d$ sheaves that are semistable with respect to a fixed polarization $H$ on $X$. When $X$ is a reduced curve the connected…

We consider the union of certain irreducible components of cohomological support loci of the canonical bundle, which we call standard. We prove a structure theorem about them and single out some particular cases, recovering and improving…

Suppose X is a smooth projective 3-fold of general type and |mK_X| is composed of a pencil of surfaces with m>1. This pencil naturally induces a fibration f:X->C onto a smooth curve C after the Stein-factorization, which is the main objects…

We study degenerations of complex projective spaces $\mathbb P^n$ into normal projective klt varieties $X$. If the tangent sheaf of $X$ is semi-stable, we show that $X$ itself is a projective space. If $X$ is a threefold with canonical…

We characterize property $(N_p)$ on a polarized surface $(X,L)$ with trivial canonical bundle in terms of the (non)existence of certain forbidden subvarieties of $X$.