Vanishing of certain equivariant distributions on spherical spaces for quasi-split groups

We prove the vanishing of $\mathfrak{z}$-eigen distributions on a quasi-split real reductive group which change according to a non-degenerate character under the left action of the unipotent radical of the Borel subgroup, and are equivariant under the right action of a spherical subgroup.     

Anticanonical system of Fano fivefolds

We show that any Fano fivefold with canonical Gorenstein singularities has an effective anticanonical divisor. Moreover, if a general element of the anticanonical system is reduced, then it has canonical singularities.     

Addendum to “Geometric invariant theory and Einstein–Weyl geometry” [Expo. Math. 29 (2) (2011) 220–230]

In this short note, we show the equivalence of the two seemingly different minitwistor space constructions of the author and N. Honda. So that this links the two articles (Honda, 2010; Kalafat, 2011) and finalizes our work.     

Counting the number of the twists of certain polarized abelian varieties

We count the number of isomorphism classes of degree d-twists of some polarized abelian varieties of dimension g over finite fields where either g is an odd prime or else $g=2$. This can be seen as a higher dimensional analogue of the counting problem for the case of elliptic curves.     

Cohomology of normal bundles of special rational varieties

Abstract

We give a new method for calculating the cohomology of the normal bundles over rational varieties which are smooth projections of Veronese embeddings. The method can be used also when the projections are not smooth, in this case it provides information about the critical locus of maps between projective spaces.     

A footnote to a theorem of Kawamata

Kawamata has shown that the quasi-Albanese map of a quasi-projective variety with log-irregularity equal to the dimension and log-Kodaira dimension 0 is birational. In this note, we show that under these hypotheses the quasi-Albanese map is proper in codimension 1 as conjectured by Iitaka.     

Abelianness of Mumford–Tate Groups Associated to Some Unitary Groups

In this paper, we investigate the action of the -cohomology of the compact dual of a compact Shimura Variety S() on the -cohomology of S()> under a cup product. We use this to split the cohomology of S() into a direct sum of (not necessarily irreducible) -Hodge structures. As an application, we prove that for the class of arithmetic subgroups of the unitary groups U(p,q) arising from Hermitian forms over CM fields, the Mumford–Tate groups associated to certain holomorphic cohomology classes on S() are Abelian. As another application, we show that all classes of Hodge type (1,1) in H² of unitary four-folds associated to the group U(2,2) are algebraic.     

All Varieties of Normal Bands with Involution

In the present paper we completely determine the lattice L(NB ^*) of all varieties of normal bands equipped with an involutorial antiautomorphism as a fundamental operation.     

Examples of Generic Lattice Ideals of Codimension 3

A commutative ring R is said to be strongly Hopfian if the chain of annihilators ann(a) ? ann(a ²) ? … stabilizes for each a ∈ R. In this article, we are interested in the class of strongly Hopfian rings and the transfer of this property from a commutative ring R to the ring of the power series R[[X]]. We provide an example of a strongly Hopfian ring R such that R[[X]] is not strongly Hopfian. We give some necessary and sufficient conditions for R[[X]] to be strongly Hopfian.