Abstract Based on the celebrated result zeros of holomorphic 1-forms complex varieties general type by Popa and Schnell, we study $n$-dimensional Kodaira dimension $n-1$. We show that a minimal smooth projective variety $X$ $\kappa (X)=\dim X-1$ admits 1-form without zero if only there is morphism from to an elliptic curve. Furthermore, for (not necessarily minimal) codimension one, give struct...

Let X be a smooth projective curve of genus g ≥ 2 defined over an algebraically closed field k of characteristic p > 0. For p sufficiently large (explicitly given in terms of r, g) we construct an atlas for the locus of all Frobenius-destabilized bundles (i.e. we construct all Frobenius-destabilized bundles of degree zero up to isomorphism). This is done by exhibiting a surjective morphism from...

K: a global function field of characteristicp # 0 E a fixed algebraic closure of K 00: a distinguished place of K A: the ring of functions in K regular away from cx> F,: a finite field which is an A-algebra VI the A-characteristic of F, (this means that the prime ideal pt, of v is the kernel of the structure morphism A + F4) 4 : a Drinfeld A-module over F, of rank d 7~: The Frobenius endomorphi...

Let $S$ be an inverse semigroup and let $E$ be its subsemigroup of idempotents. In this paper we define the $n$-th module cohomology group of Banach algebras and show that the first module cohomology group $HH^1_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is zero, for every odd $ninmathbb{N}$. Next, for a Clifford semigroup $S$ we show that $HH^2_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is a Banach sp...

Let $R$ be a commutative Noetherian ring with non-zero identity, $fa$ an ideal of $R$, and $X$ an $R$--module. Here, for fixed integers $s, t$ and a finite $fa$--torsion $R$--module $N$, we first study the membership of $Ext^{s+t}_{R}(N, X)$ and $Ext^{s}_{R}(N, H^{t}_{fa}(X))$ in the Serre subcategories of the category of $R$--modules. Then, we present some conditions which ensure the exi...

Let (X,D) be a D-scheme in the sense of Beilinson and Bernstein, given by an algebraic variety X and a morphism OX → D of sheaves of rings on X. We consider noncommutative deformations of quasi-coherent sheaves of left D-modules on X, and show how to compute their pro-representing hulls. As an application, we compute the noncommutative deformations of the left DX -module OX when X is any ellipt...

Inspired by the classical theory of modules over a monoid, we give a first account of the natural notion of module over a monad, which encompasses the notion of algebra. The associated notion of morphism of modules (”linear” natural transformations) captures important formal properties about substitution. In this paper, we present basic constructions of modules and we show examples concerning i...

We address the problem of deening an algebraic framework for modularization supporting separate type-checking. In order to do that we introduce the notions of abstract type system and logic of constraints and we present a canonical construction of a model part, on top of a logic of constraints. This canonical construction works under standard assumptions on the underlying type system. We show t...

For two normed algebras $A$ and $B$ with the character space   $bigtriangleup(B)neq emptyset$  and a left $B-$module $X,$  a certain class of bounded linear maps from $A$ into $X$ is introduced. We set $CMH_B(A, X)$  as the set of all non-zero $B-$character module homomorphisms from $A$ into $X$. In the case where $bigtriangleup(B)=lbrace varphirbrace$ then $CMH_B(A, X)bigcup lbrace 0rbrace$ is...

LF has been designed and successfully used as a meta-logical framework to represent and reason about object logics. Here we design a representation of the Isabelle logical framework in LF using the recently introduced module system for LF. The major novelty of our approach is that we can naturally represent the advanced Isabelle features of type classes and locales. Our representation of type c...