We define tautological Chow classes on the moduli space G d of triples consisting of a curve C, a line bundle L on C of degree d, and a linear system V on L of dimension r. In the case where the forgetful morphism to Mg has relative dimension zero, we describe the images of these classes in A(Mg). As an application, we compute the (virtual) slopes of several different classes of divisors on Mg.

Given a characteristic zero field k and a dominant morphism of affine algebraic k-groups μ : G → C one can form a functor from k-algebras to abelian groups R 7→ F(R) := C(R)/μ(G(R)). Assuming that C is commutative we prove that this functor satisfies a purity theorem for any regular local k-algebra. Few examples are considered in the very end of the preprint.

Abstract We describe all polarizations for abelian varieties over a finite field in fixed isogeny class corresponding to squarefree Weil polynomial, when one variety the admits canonical lifting characteristic zero, that is, which reduction morphism induces an isomorphism of endomorphism rings. Categorical equivalences between fields and fractional ideals étale algebras enable us explicitly com...

In this short note, we will show the following weak evidence of S. Lang conjecture over function elds. Let f : X ! Y be a projective and surjective morphism of algebraic varieties over an algebraically closed eld k of characteristic zero, whose generic ber is geometrically irreducible and of general type. If f is not birationally trivial, then there are countably many proper closed varieties fZ...

An unpublished result by the first author states that there exists a Hopf algebra H such that for any Möbius category C (in the sense of Leroux) there exists a canonical algebra morphism from the dual H∗ of H to the incidence algebra of C. Moreover, the Möbius inversion principle in incidence algebras follows from a ‘master’ inversion result in H∗. The underlying module of H was originally defi...

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 $s$ 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 space,...

Data Type – Each value is some data object – Operations are implemented separately in a generic module – Same module shared by all the values belonging to each type Object-Oriented Approach DoubleRing := proc(val::float) local Me; Me := module() export v, a, s, m, d, gt, zero, one, coerce, absolute, sine, sqroot; v := val; # Data value of object # Implementations for +, -, *, /, >, etc a := (b)...

Let G be a reductive algebraic group and H a closed subgroup of G. Explicit constructions of G-invariant ideals in the algebra K[G/H] are given. This allows to obtain an elementary proof of Matsushima’s criterion: a homogeneous space G/H is an affine variety if and only if H is reductive. 1. Algebraic homogeneous spaces Let G be an affine algebraic group over an algebraically closed field K. A ...