Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

완효성 비료와 4종복비의 혼용 시용이 팔레놉시스의 생육에 미치는 효과

In the gauge theory approach to the geometric Langlands program, ramification can be described in terms of "surface operators," which are supported on two-dimensional surfaces somewhat as Wilson or 't Hooft operators are supported on curves. We describe the relevant surface operators in N=4 super Yang-Mills theory, and the parameters they depend on, and analyze how S-duality acts on these parameters. Then, after compactifying on a Riemann surface, we show that the hypothesis of S-duality for surface operators leads to a natural extension of the geometric Langlands program for the case of tame ramification. The construction involves an action of the affine Weyl group on the cohomology of the moduli space of Higgs bundles with ramification, and an action of the affine braid group on A-branes or B-branes on this space.

https://www.intlpress.com/site/pub/files/_fulltext/journals/cdm/2006/2006/0001/CDM-2006-2006-0001-a002.pdf

Gauge Theory, Ramification, And The Geometric Langlands Program

In the gauge theory approach to the geometric Langlands program, ramification can be described in terms of ``surface operators,'' which are supported on two-dimensional surfaces somewhat as Wilson or 't Hooft operators are supported on curves. We describe the relevant surface operators in N=4 super Yang-Mills theory, and the parameters they depend on, and analyze how S-duality acts on these parameters. Then, after compactifying on a Riemann surface, we show that the hypothesis of S-duality for surface operators leads to a natural extension of the geometric Langlands program for the case of tame ramification. The construction involves an action of the affine Weyl group on the cohomology of the moduli space of Higgs bundles with ramification, and an action of the affine braid group on A-branes or B-branes on this space.

Resume Soient X une courbe complexe, lisse, projective et connexe et G un groupe algebrique complexe, simple et simplement connexe. Nous calculons le groupe de Picard du champ des G-fibres quasi-paraboliques sur X, decrivons explicitement ses generateurs pour G de type classique ou G2, puis identifions les espaces de sections globales correspondants avec les espaces de vacua de Tsuchiya, Ueno et Yamada. La methode utilise le theoreme d'uniformisation qui decrit ces champs comme doubles quotients de certains groupes algebriques de dimension infinie. Nous decrivons le fibre dualisant du champ des G-fibres et montrons qu'il admet une unique racine carree, que nous construisons explicitement. Si G n'est pas simplement connexe, la racine carree depend du choix d'une theta-caracteristique. Ces resultats sur les champs permettent de retrouver le theoreme de Drezet et Narasimhan (pour l'espace de modules grossier) et de montrer un enonce analogue dans le cas G = Sp2r. Nous montrons aussi que le module grossier des SOr-fibres n'est pas localement factoriel pour r ≥ 7.

The line bundles on the moduli of parabolic G-bundles over curves and their sections

Espaces de modules de fibrés paraboliques et blocs conformes

Let X be a smooth projective curve over a field of characteristic p > 0. We show that the Hitchin morphism, which associates to a Higgs bundle its characteristic polynomial, has a nontrivial deformation over the affine line. This deformation is constructed by considering the moduli stack of t-connections on vector bundles on X and an analogue of the p-curvature, and by observing that the associated characteristic polynomial is, in a suitable sense, a p th -power.

/pdf/on-the-hitchin-morphism-in-positive-characteristic-zcfebq6sml.pdf

On the Hitchin morphism in positive characteristic

Let X be a smooth projective curve of genus g ≥ 2 over an algebraically closed field k of characteristic p > 0. Let MX be the moduli space of semistable rank-2 vector bundles over X with trivial determinant. The relative Frobenius map F : X → X1 induces by pull-back a rational map V : MX1 99K MX. In this paper we show the following results. (1) For any line bundle L over X, the rank-p vector bundle FL is stable. (2) The rational map V has base points, i.e., there exist stable bundles E over X1 such that FE is not semistable. (3) Let B ⊂ MX1 denote the scheme-theoretical base locus of V. If g = 2, p > 2 and X ordinary, then B is a 0-dimensional local complete intersection of length 2 p(p 2 − 1) and the degree of V equals 1 p(p 2 + 2).

https://math.unice.fr/%7Epauly/frobeniusdestabilized.pdf

On Frobenius-destabilized rank-2 vector bundles over curves

The moduli space M0 of semi-stable rank 2 vector bundles with fixed trivial determinant over a non-hyperelliptic curve C of genus 3 is isomorphic to a quartic hypersurface in P 7 (Coble’s quartic). We show that M0 is self-dual and that its polar map associates to a stable bundle E ∈ M0 a bundle F which is characterized by dim H 0 (C, E ⊗ F) = 4. The projective

/pdf/self-duality-of-coble-s-quartic-hypersurface-and-50vuuqu23b.pdf

Self-duality of Coble's quartic hypersurface and applications

Let $X$ be an ordinary smooth curve defined over an algebraically closed field of characteristic 2. The absolute Frobenius induces a rational map $F$ on the moduli space $M_X$ of rank 2 vector bundles with fixed trivial determinant. If the genus of $X$ is 2, the moduli space $M_X$ is isomorphic to projective space of dimension 3 (as over the complex numbers). In this case we explicitly give the equations of $F$, which enables us to determine, for example, its base locus (one point) and its image (different from $M_X$).

Christian Pauly

Papers

Espaces de modules de fibrés paraboliques et blocs conformes

On the Hitchin morphism in positive characteristic

On Frobenius-destabilized rank-2 vector bundles over curves

Self-duality of Coble's quartic hypersurface and applications

The action of the Frobenius map on rank 2 vector bundles in characteristic 2