Related papers: Line Bundles on The First Drinfeld Covering

We use Totaro's examples of non-semiample nef line bundles on smooth projective surfaces over finite fields to construct nef line bundles for which the first cohomology group cannot be killed by any generically finite covers. This is used…

In this paper, we construct new characteristic classes of fiber bundles via flat connections with values in infinite-dimensional Lie algberas of derivations. In fact, choosing a fiberwise metric, we construct a chain map to the de Rham…

Infinitesimal symmetries of $S^1$-bundle gerbes are modelled with multiplicative vector fields on Lie groupoids. It is shown that a connective structure on a bundle gerbe gives rise to a natural horizontal lift of multiplicative vector…

Let $\Mg$ denote the moduli space of compact Riemann surfaces of genus $g$. Mumford had proved that, for each fixed genus $g$, there are isomorphisms asserting that certain higher $DET$ bundles over $\Mg$ are certain fixed…

Let $X$ be a compact connected Riemann surface, $D\, \subset\, X$ a reduced effective divisor, $G$ a connected complex reductive affine algebraic group and $H_x\, \subsetneq\, G_x$ a Zariski closed subgroup for every $x\, \in\, D$. A framed…

Let $\Phi $ be a Drinfeld $\mathbf{F}_{q}[T]$-module of rank 2, over a finite field $L$, a finite extension of $n$ degrees for a finite field with $q$ elements $% \mathbf{F}_{q}$. Let $P_{\Phi}(X)=$ $X^{2}-cX+\mu P^{m}$ ($c$ an element of…

We prove that the tangent bundle of a generic space of planar n-gons with specified side lengths, identified under isometry, plus a trivial line bundle is isomorphic to (n-2) times a canonical line bundle. We then discuss consequences for…

Let $B$ be a simply-connected projective variety such that the first cohomology groups of all line bundles on $B$ are zero. Let $E$ be a vector bundle over $B$ and $X={\mathbb P} (E)$. It is easily seen that a power of any endomorphism of…

We deal with first-order definability in the embeddability ordering $( \mathcal{D}; \leq)$ of finite directed graphs. A directed graph $G\in \mathcal{D}$ is said to be embeddable into $G' \in \mathcal{D}$ if there exists an injective graph…

We show that every Lie algebroid $A$ over a manifold $P$ has a natural representation on the line bundle $Q_A = \wedge^{top}A \otimes \wedge^{top} T^*P$. The line bundle $Q_A$ may be viewed as the Lie algebroid analog of the orientation…

Using the existence of certain symplectic submanifolds in symplectic 4-manifolds, we prove an estimate from above for the number of singular fibers with separating vanishing cycles in minimal Lefschetz fibrations over surfaces of positive…

Let $X$ be a compact Riemann surface of genus $g \geq 3$ and $S$ a finite subset of $X$. Let $\xi$ be fixed a holomorphic line bundle over $X$ of degree $d$. Let $\mathcal{M}_{pc}(r, d, \alpha)$ (respectively, $\mathcal{M}_{pc}(r, \alpha,…

Let M be a closed enlargeable spin manifold. We show non-triviality of the universal index obstruction in the K-theory of the maximal $C^*$-algebra of the fundamental group of M. Our proof is independent from the injectivity of the…

If E is a C^\infty complex vector bundle on an oriented C^\infty manifold \Sigma, diffeomorphic to a circle, then the space of sections of E has a canonical polarization in the sense of Pressley and Segal and so one has its determinantal…

Let $\Omega$ be the complement of a connected, essential hyperplane arrangement. We prove that every dominant endomorphism of $\Omega$ extends to an endomorphism of the tropical compactification $X$ of $\Omega$ associated to the Bergman fan…

We show the following symmetry property of a bounded Reinhardt domain $\Omega$ in $\mathbb{C}^{n+1}$: let $M=\partial\Omega$ be the smooth boundary of $\Omega$ and let $h$ be the Second Fundamental Form of $M$; if the coefficient $h(T,T)$…

This submission replaces the arXiv:1012.5381 submission with the same title, which had been withdrawn as it contained a mistake, repaired in this submission: on $X$ projective smooth over an algebraically closed field of characteristic…

The principal filtration of the infinite-dimensional odd Contact Lie superalgebra over a field of characteristic $p>2$ is proved to be invariant under the automorphism group by investigating ad-nilpotent elements and determining certain…

This article is based on the methods developed in [AGG]. We construct a complex hyperbolic structure on a trivial disc bundle over a closed orientable surface $\Sigma$ (of genus 2) thus solving a long standing problem in complex hyperbolic…

We introduce new families of quandles that serve as invariants for classifying closed orientable surfaces. These families generalize the classical Dehn quandle and are defined, respectively, on isotopy classes of unoriented closed curves…