Slanted Vector Fields for Jet Spaces

Low pole order frames of slanted vector fields are constructed on the space of vertical k-jets of the universal family of complete intersections in $\mathbb{P}^n$ and, adapting the arguments, low pole order frames of slanted vector fields are also constructed on the space of vertical logarithmic k-jets along the universal family of projective hypersurfaces in $\mathbb{P}^n$ with several irreducible smooth components. Both the pole order (here $=5k-2$) and the determination of the locus where the global generation statement fails are improved compared to the literature (previously $=k^2+2k$), thanks to three new ingredients; we reformulate the problem in terms of some adjoint action, we introduce a new formalism of geometric jet coordinates, and then we construct what we call building-block vector fields, making the problem for arbitrary jet order $k\geqslant1$ into a very analog of the much easier case where $k=0$, i.e. where no jet coordinates are needed.Comment: 26 pages, comments are welcome. (v3 : major overhaul

Fiber integration on the Demailly tower

The goal of this work is to provide a fiber integration formula on the Demailly tower, that avoids step-by-step elimination of horizontal cohomology classes, and that yields computational effectivity. A natural twist of the Demailly tower is introduced and a recursive formula for the total Segre class at k-th level is obtained. Then, by interpreting single Segre classes as coefficients, an iterated residue formula is derived.Comment: 22 pages, to appear in Annales de l'Institut Fourie

Gysin maps, duality and Schubert classes

We establish a Gysin formula for Schubert bundles and a strong version of the duality theorem in Schubert calculus on Grassmann bundles. We then combine them to compute the fundamental classes of Schubert bundles in Grassmann bundles, which yields a new proof of the Giambelli formula for vector bundles.Comment: Version 3: published versio

Complete intersection varieties with ample cotangent bundles

Any smooth projective variety contains many complete intersection subvarieties with ample cotangent bundles, of each dimension up to half its own dimension.Comment: Reader-friendly version, to appear in Inventiones Mathematica

Supervisory Control for Modal Specifications of Services

International audienceIn the service oriented architecture framework, a modal specification, as defined by Larsen in \cite{Lar89}, formalises how a service should interact with its environment. More precisely, a modal specification determines the events that the server may or must allow at each stage in an interactive session. Therefore, techniques to enforce a modal specification on a system would be useful for practical applications. In this paper, we investigate the adaptation of the supervisory control theory of Ramadge and Wonham to enforce a modal specification (with final states marking the ends of the sessions) on a system modelled by a finite LTS. We prove that there exists at most one most permissive solution to this control problem. We also prove that this solution is regular and we present an algorithm for the effective computation of the corresponding controlle

Quasi-positive orbifold cotangent bundles ; Pushing further an example by Junjiro Noguchi

In this work, we investigate the positivity of logarithmic and orbifold cotangent bundles along hyperplane arrangements in projective spaces. We show that a very interesting example given by Noguchi (as early as in 1986) can be pushed further to a very great extent. Key ingredients of our approach are the use of Fermat covers and the production of explicit global symmetric differentials. This allows us to obtain some new results in the vein of several classical results of the literature on hyperplane arrangements. These seem very natural using the modern point of view of augmented base loci, and working in Campana's orbifold category. As an application of our results, we derive two new orbifold hyperbolicity results, going beyond some classical results of value distribution theory.Comment: V2: better formulation of the genericity condition, thanks to an indication of Fr\'ed\'eric Ha

Petri Net Reachability Graphs: Decidability Status of FO Properties

We investigate the decidability and complexity status of model-checking problems on unlabelled reachability graphs of Petri nets by considering first-order, modal and pattern-based languages without labels on transitions or atomic propositions on markings. We consider several parameters to separate decidable problems from undecidable ones. Not only are we able to provide precise borders and a systematic analysis, but we also demonstrate the robustness of our proof techniques