相关论文: Logarithmic Jet Bundles and Applications

We prove that the complement of a very generic curve of degree $d$ at least equal to 15 in the projective plane is hyperbolic in the sens of Kobayashi (here, the terminology ``very generic'' refers to complements of countable unions of…

We define and study jet bundles in the geometric orbifold category. We show that the usual arguments from the compact and the logarithmic settings do not all extend to this more general framework. This is illustrated by simple examples of…

We give a fully algebraic proof of an important theorem of Demailly, stating the existence of many Green-Griffiths jet differentials on a complex projective manifold of general type. To this end, we introduce a new algebraic version of the…

This thesis establishes a geometric approach to the de Rham realization of the polylogarithm. As a central result we construct the logarithm sheaves of rational abelian schemes in terms of the birigidified Poincar\'e bundle with universal…

The study of entire holomorphic curves contained in projective algebraic varieties is intimately related to fascinating questions of geometry and number theory -- especially through the concepts of curvature and positivity which are central…

We introduce logarithmic Picard algebroids, a natural class of Lie algebroids adapted to a simple normal crossings divisor on a smooth projective variety. We show that such algebroids are classified by a subspace of the de Rham cohomology…

We prove that the category of vector bundles over a fixed smooth manifold and its corresponding category of convenient modules are models for intuitionistic differential linear logic. The exponential modality is modelled by composing the…

We propose an approach to study logarithmic sheaves T(-log A) associated with a hyperplane arrangements A on the projective space, based on projective duality, direct image functors and vector bundles methods. We focus on freeness of line…

We discuss the Morse estimates for the curvature of several metrics on Semple weighted projective bundle over a projective variety. Following Demailly works on holomorphic Morse inequalities we show an analogue of his results along the…

Let $(X, \omega)$ be a weakly pseudoconvex K\"ahler manifold, $Y \subset X$ a closed submanifold defined by some holomorphic section of a vector bundle over $X,$ and $L$ a Hermitian line bundle satisfying certain positivity conditions. We…

Motivated by conjectures of Demailly, Green-Griffiths, Lang, and Vojta, we show that several notions related to hyperbolicity behave similarly in families. We apply our results to show the persistence of arithmetic hyperbolicity along field…

We formulate and prove the existence of an asymptotic duality along the fibers of the Green-Griffiths jet bundles over projective manifolds. The existence of global sections for these bundles and also for their dual sheaves has been…

The theory of relative logarithmic jet spaces is developed for log schemes. With this theory the existence of bounds of intersection multiplicities of curves and divisors on certain log schemes is established. This result extends those of…

We generalize the Demailly approximation theorem from complex geometry to Arakelov geometry.As an application, let $X/\mathbb{Q}$ be an integral projective variety and $\overline N$ be an adelic line bundle on $X$, we prove that…

Jet manifolds and vector bundles allow one to employ tools of differential geometry to study differential equations, for example those arising as equations of motions in physics. They are necessary for a geometrical formulation of…

This is a remastered and expanded version of a an earlier preprint of the author, in which we give a fully algebraic proof of an important theorem of Demailly, stating the existence of many Green-Griffiths jet differentials on a complex…

Let D = {D_{1},...,D_{l}} be an arrangement of smooth hypersurfaces with normal crossings on the complex projective space P^n and let \Omega^{1}_{P^n}(log D) be the logarithmic bundle attached to it. Following [1], we show that…

In this paper, we prove a $\partial\bar{\partial}$-type lemma on compact K\"ahler manifolds for logarithmic differential forms valued in the dual of a certain pseudo-effective line bundle, thereby confirming a conjecture proposed by X. Wan.…

We introduce the concept of directed orbifold, namely triples (X, V, D) formed by a directed algebraic or analytic variety (X, V), and a ramification divisor D, where V is a coherent subsheaf of the tangent bundle TX. In this context, we…

In this paper we state and prove some results on the structure of the jetbundles as left and right module over the structure sheaf on the projective line and projective space using elementary techniques involving diagonalization of…