Related papers: Projectively flat log smooth pairs

Let $k$ be a perfect field, and $X$ an irreducible smooth projective curve over $k$. We give a criterion for a vector bundle over $X$ to admit a logarithmic connection singular over a finite subset of $X$ with given residues, where residues…

We show that there exists a fine moduli space for torsion-free sheaves on a projective surface, which have a "good framing" on a big and nef divisor. This moduli space is a quasi-projective scheme. This is accomplished by showing that such…

A map of fine log schemes $X \to Y$ induces a map from the scheme underlying $X$ to Olsson's algebraic stack of strict morphisms of fine log schemes over $Y$. A sheaf on $X$ is called \emph{log flat over} $Y$ iff it is flat over this…

We give a criterion for a flat fibration with affine plane fibers over a smooth scheme defined over a field of characteristic zero to be a Zariski locally trivial $\mathbb{A}^2$-bundle. An application is a positive answer to a version of…

In this article, we introduce the logarithmic de Rham stack of a pair (X, D), for a smooth variety X over a field k of positive characteristic p, and D a strict normal crossings divisor on X. Using this stack, we prove a new version of…

Let $\mathbb{X}$ be a Geigle-Lenzing projective plane of type $(2,2,2,p)$ and $\mathsf{coh} \mathbb{X}$ the category of coherent sheaves on $\mathbb{X}$. This paper is devoted to study ACM tilting bundles over $\mathbb{X}$, that is, tilting…

We show that an abelian surface embedded in P^N by a very ample line bundle L of type (1,2d) is projectively normal if and only if d>=4. This completes the study of the projective normality of abelian surfaces embedded by complete linear…

This is the first in a pair of papers developing a framework for the application of logarithmic structures in the study of singular curves of genus $1$. We construct a smooth and proper moduli space dominating the main component of…

We study smooth projective complex varieties with ample cotangent bundle. Our main result is that in an abelian variety of dimension n, a complete intersection of at least n/2 general hypersurfaces of sufficiently high degrees has ample…

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…

Let $G$ be a simple simply-connected connected linear algebraic group over $\mathbb{C}$. We proved a $2$-birational Torelli theorem for the moduli space of semistable principal $G$-bundles over a smooth curve of genus $\geq 3$, which says…

We study the proalgebraic space which is the inverse limit of all finite branched covers over a normal toric variety with branching set the invariant divisor under the algebraic torus action. These are completions (compactifications) of the…

We construct examples of flat fiber bundles over the Hopf surface such that the total spaces have no pseudoconvex neighborhood basis, admit a complete K\"ahler metric, or are hyperconvex but have no nonconstant holomorphic functions. For…

Let X be a smooth projective curve of genus at least two over the complex numbers. A pair (E,\phi) over X consists of an algebraic vector bundle E over X and a holomorphic section \phi of E. There is a concept of stability for pairs which…

We construct proper good moduli spaces for moduli stacks of Bridgeland semistable orthosymplectic complexes on a complex smooth projective variety, which we propose as a candidate for compactifying moduli spaces of principal bundles for the…

Multi-scale differentials were constructed by M.~Bainbridge, D.~Chen, Q.~Gendron, S.~Grushevsky, and M.~M\"oller, from the viewpoint of flat and complex geometry, for the purpose of compactifying moduli spaces of curves together with a…

Let $X$ be a projective toric variety of dimension $n$ and let $L$ be a ample line bundle on $X$. For $k \geq 0$, it is in general difficult to determine whether $L^{\otimes k}$ is very ample and whether it additionally gives a projectively…

Given an essentially finite type morphism of schemes f: X --> Y and a positive integer d, let f^{d}: X^{d} --> Y denote the natural map from the d-fold fiber product, X^{d}, of X over Y and \pi_i: X^{d} --> X the i'th canonical projection.…

We consider those projective bundles (or Brauer-Severi varieties) over an abelian variety that are homogeneous, i.e., invariant under translation. We describe the structure of these bundles in terms of projective representations of…

We show that there exist flat surface bundles with closed leaves having non-trivial normal bundles. This leads us to compute the Abelianisation of surface diffeomorphism groups with marked points. We also extend a formula of Tsuboi that…