For conic bundles on a smooth variety (over a field of characteristic 6= 2) which degenerate into pairs of distinct lines over geometric points of a smooth divisor, we prove a theorem which relates the Brauer class of the non-degenerate conic on the complement of the divisor to the covering class (Kummer class) of the 2-sheeted cover of the divisor defined by the degenerate conic, via the Gysin...

For a rank two vector bundle E on the projective plane IP the divisor DE of its jumping lines is a certain generalization of the Chow divisor of a projective scheme We give a generalization of this divisor for coherent sheaves on surfaces Using this duality we construct the moduli space of coherent sheaves on a surface that does not use Mumford s geometric invariant theory Furthermore we obtain...

We study slope stability of smooth surfaces and its connection with exceptional divisors. We show that a surface containing an exceptional divisor with arithmetic genus at least two is slope unstable for some polarisation. In the converse direction we show that slope stability of surfaces can be tested with divisors, and prove that for surfaces with non-negative Kodaira dimension any destabilis...

Abstract. A sum divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1,2,...,| ( ) |} V G such that each edge uv assigned the label 1 if 2 divides ( ) ( ) f u f v + and 0 otherwise. Further, the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a sum divisor cordial labeling is called a sum divisor cordial grap...

In the noncommutative geometry of Artin, Van den Bergh, and others, the twisted homogeneous coordinate ring is one of the basic constructions. Such a ring is defined by a σ-ample divisor, where σ is an automorphism of a projective scheme X. Many open questions regarding σ-ample divisors have remained. We derive a relatively simple necessary and sufficient condition for a divisor on X to be σ-am...

In the noncommutative geometry of Artin, Van den Bergh, and others, the twisted homogeneous coordinate ring is one of the basic constructions. Such a ring is defined by a σ-ample divisor, where σ is an automorphism of a projective scheme X. Many open questions regarding σ-ample divisors have remained. We derive a relatively simple necessary and sufficient condition for a divisor on X to be σ-am...

The idea of associating a graph with the zero-divisors of a commutative ring was originated by Beck. The problems concerning zero-divisor graphs have been studied extensively in the past 10 years. DeMeyer and DeMeyer presented some properties for the correspondence between zero-divisor graphs and their semigroups. It is very important to have adequate examples before the complete resolution of ...

We give a local deformation theoretic proof of Farkas’ conjecture that a principally polarized complex abelian variety of dimension 4 whose theta divisor has an isolated double point of rank 3 at a point of order two is a Jacobian. The argument yields an explicit local normal form for the theta function near such a point. The proof depends only on the facts that the theta function is even, a ge...

Let C be a curve over a complete valued field with infinite residue field whose skeleton is a chain of loops with generic edge lengths. We prove that any divisor on the chain of loops that is rational over the value group lifts to a divisor of the same rank on C, confirming a conjecture of Cools, Draisma, Robeva, and the third author.

For homogeneous simply connected Hodge manifolds it is proved that the set of coherent vectors orthogonal to a given one is the divisor responsible for the homogeneous holomorphic line bundle of the coherent vectors. In particular, for naturally reductive spaces, the divisor is the cut locus.