This paper deals with some results concerning the notion of extended ideal based zero divisor graph $overline Gamma_I(R)$ for an ideal $I$ of a commutative ring $R$ and characterize its bipartite graph. Also, we study the properties of an annihilator of $overline Gamma_I(R)$.

Abstract We prove the integral Hodge conjecture for curve classes on smooth varieties of dimension at least three constructed as a complete intersection ample hypersurfaces in projective toric variety, such that anticanonical divisor is restriction nef divisor. In particular, this includes case Fano varieties. fact, using results Casagrande and minimal model program, we each case, generated by ...

The moduli space Mg,n of n−pointed stable curves of genus g is stratified by the topological type of the curves being parametrized: the closure of the locus of curves with k nodes has codimension k. The one dimensional components of this stratification are smooth rational curves (whose numerical equivalence classes are) called F−curves. These are believed to determine all ample divisors: F−Conj...

We investigate the symplectic geometric and also differential aspects of moduli space connections on a compact connected Riemann surface X . Fix theta characteristic K 1 / 2 ; it defines divisor M stable vector bundles rank r degree zero. Given bundle E ? lying outside divisor, we construct natural holomorphic connection that depends holomorphically Using this connection, canonical isomorphism ...

A metric graph is a geometric realization of a finite graph by identifying each edge with a real interval. A divisor on a metric graph Γ is an element of the free abelian group on Γ. The rank of a divisor on a metric graph is a concept appearing in the RiemannRoch theorem for metric graphs (or tropical curves) due to Gathmann and Kerber [7], and Mikhalkin and Zharkov [10]. We define a rank-dete...

Let M be a commutative cancellative monoid. The set ∆(M), which consists of all positive integers which are distances between consecutive irreducible factorization lengths of elements in M , is a widely studied object in the theory of nonunique factorizations. If M is a Krull monoid with divisor class group Zn, then it is well-known that ∆(M) ⊆ {1, 2, . . . , n − 2}. Moreover, equality holds fo...

If S is a Krull monoid with finitely generated divisor class group such that only finitely many divisor classes of S contain prime divisors, then we construct an algorithm to compute the elasticity of S. © 2001 Elsevier Science Inc. All rights reserved. AMS classification: 20M14; 20M25; 13F05; 11Y05

orbit closure, 32 character, 33cone, 9dual, 10lattice, 10strongly convex, 10convex function, 42 distinguished point, 28divisorCartier, 38T -invariant, 40principal, 39prime, 37Weil, 37T -invariant, 39principal, 38divisor class group, 38

The Chern class of the sheaf of logarithmic derivations along a simple normal crossing divisor equals the Chern-Schwartz-MacPherson class of the complement of the divisor. We extend this equality to more general divisors, which are locally analytically isomorphic to free hyperplane arrangements.

Introduction: A good understanding of the geometry of a theta divisor Θ of a principally polarized abelian variety (A,Θ) requires a knowledge of properties of its canonical linear system, the Gauss linear system |OΘ(Θ)|. A striking feature of the theta divisor Θ(C) of the Jacobian of a curve C is that the dual of the branch divisor of the associated Gauss map γΘ on Θ, is not a hypersurface as e...