Let X be a projective scheme over a finite field. In this paper, we consider the asymptotic behavior of the number of effective cycles on X with bounded degree as it goes to the infinity. By this estimate, we can define a certain kind of zeta functions associated with groups of cycles. We also consider an analogue in Arakelov geometry. Introduction Let X be a projective scheme over a finite fie...

The coordinate projective line over a field is seen as a groupoid with a further ‘projection’ structure. We investigate conversely to what extent such an, abstractly given, groupoid may be coordinatized by a suitable field constructed out of the geometry.

Using a general result of Lusztig, we find the decomposition into irreducibles of certain induced characters of the projective general linear group over a finite field of odd characteristic.

Let A be a finite dimensional unitary algebra over an algebraically closed field K. Here we study the vector bundles on a smooth projective curve which are equipped with a faithful action of A.

Abstract We construct a Kawamata type semiorthogondal decomposition for the bounded derived category of coherent sheaves nodal quintic del Pezzo threefolds, decomposing into categories finite dimensional algebras. This is achieved by constructing birational maps from threefolds to quadric surface fibrations over projective line.

A Sylvester-Gallai (SG) configuration is a finite set S of points such that the line through any two points in S contains a third point of S. According to the Sylvester-Gallai Theorem, an SG configuration in real projective space must be collinear. A problem of Serre (1966) asks whether an SG configuration in a complex projective space must be coplanar. This was proved by Kelly (1986) using a d...

We study two different actions on the moduli spaces of logarithmic connections over smooth complex projective curves. Firstly, we establish a dictionary between logarithmic orbifold connections and parabolic logarithmic connections over the quotient curve. Secondly, we prove that fixed points on the moduli space of connections under the action of finite order line bundles are exactly the push-f...

The study of blocking semiovals in finite projective planes was motivated by Batten [1] in connection with cryptography. Dover in [4] studied blocking semiovals in a finite projective plane of order q which meet some line in q − 1 points. In this note, some blocking semiovals in PG(2, q) are considered which admit a homology group, and three new families of blocking semiovals are constructed. A...

1 Motivation In the whole paper K is a field of finite type over its prime field K 0 of characteristic p ≥ 0 and not equal to 2. As typical case we can take K as number field or as function field of one variable over a finite field. With K s we denote its separable closure. With n we denote an odd number larger than 5 and prime to p. We begin by stating three motivations. Let C be a smooth proj...