Related papers: Jet bundles on projective space II

Let $p$ be a prime. This papers aims at investigating sheaf cohomology of a broader class of $p$-adic period domains, other then the Drinfeld's upper half space (cf. \cite{O2}). Concretely, we let $\mathbf{G}$ be a split connected reductive…

Let X be a non-singular algebraic curve of genus at least 3 and let M denote the moduli space of stable vector bundles of rank n and fixed determinant of degree d with n and d coprime. For any semistable bundle E over X, we can pull E back…

Applying Robert Boltje's theory of canonical induction, we give a restriction-preserving formula expressing any $p$-permutation module as a $\mathbb{Z}[1/p]$-linear combination of modules induced and inflated from projective modules…

In this paper, the first of a series of three, we classify holomorphic principal G-bundles over an elliptic curve, where G is a reductive group. We also study the local and global properties of the moduli space of semistable G-bundles. We…

For a commutative algebra $A$ over $\mathbb{C}$,denote $\mathfrak{g}=\text{Der}(A)$. A module over the smash product $A\# U(\mathfrak{g})$ is called a jet $\mathfrak{g}$-module, where $U(\mathfrak{g})$ is the universal enveloping algebra of…

Let X be a nonsingular projective algebraic curve of genus g\ge3. We consider the moduli space M of stable bundles of fixed determinant with rank n and degree d coprime and d>n(2g-2). There is a universal bundle on XxM and we consider the…

Suppose $(X, g)$ is a compact, spin Riemannian 7-manifold, with Dirac operator $D$. Let $G$ be SU$(m)$ or U$(m)$, and $E\to X$ be a rank $m$ complex bundle with $G$-structure. Write ${\mathcal B}_E$ for the infinite-dimensional moduli space…

Let $M$ be the moduli space of generalized parabolic bundles (GPBs) of rank $r$ and degree $d$ on a smooth curve $X$. Let $M_{\bar L}$ be the closure of its subset consisting of GPBs with fixed determinant ${\bar L}$. We define a moduli…

In this paper we prove a refined version of the canonical key formula for projective abelian schemes in the sense of Moret-Bailly, we also extend this discussion to the context of Arakelov geometry. Precisely, let $\pi: A\to S$ be a…

We consider the moduli space of stable principal G-bundles over a compact Riemann surface C of genus >1, with G a reductive algebraic group. We explicitly construct a map F from the generic fibre of the Hitchin map to a generalized Prym…

We give a geometric interpretation of the Weil representation of the metaplectic group, placing it in the framework of the geometric Langlands program. For a smooth projective curve X we introduce an algebraic stack \tilde\Bun_G of…

Let G be an affine reductive algebraic group over an algebraically closed field k. We determine the Picard group of the moduli stacks of principal G-bundles on any smooth projective curve over k.

Let G be a linear algebraic group over an algebraically closed field of characteristic p whose corresponding root system is irreducible. In this paper we calculate the Weyl filtration dimension of the induced G-modules, \nabla(\lambda) and…

We introduce a new method to study mixed characteristic deformation of line bundles. In particular, for sufficiently large smooth projective families $f : \mathscr{X} \to \mathscr{S}$ defined over the ring of $N$-integers…

This paper continues the study of holomorphic semistable principal G-bundles over an elliptic curve. In this paper, the moduli space of all such bundles is constructed by considering deformations of a minimally unstable G-bundle. The set of…

Let $H$ be a semisimple algebraic group. We prove the semistable reduction theorem for $\mu$--semistable principal $H$--bundles over a {\it smooth projective variety $X$} defined over the field $\bc$. When $X$ is a {\it smooth projective…

Let $X$ be a smooth projective connected curve of genus $g\ge 2$ defined over an algebraically closed field $k$ of characteristic $p>0$. Let $G$ be a finite group, $P$ a Sylow $p$-subgroup of $G$ and $N_G(P)$ its normalizer in $G$. We show…

We exhibit a relationship between projective duality and the sheaf of logarithmic vector fields along a reduced divisor $D$ of projective space, in that the push-forward of the ideal sheaf of the conormal variety in the point-hyperplane…

Given a scheme $Y$ equipped with a collection of globally generated vector bundles $E_1, \dots, E_n$, we study the universal morphism from $Y$ to a fine moduli space $\mathcal{M}(E)$ of cyclic modules over the endomorphism algebra of…

For a smooth canonically embedded curve $C$ of genus $9$ together with a pencil $|L|$ of degree $6$, we study the relative canonical resolution of $C\subset X\subset \mathbb{P}^8$, where $X$ is the scroll swept out by the pencil $|L|$. We…