Abstract Let X be a semistable curve and L line bundle whose multidegree is uniform, i.e., in the range between those of structure sheaf dualizing . We establish an upper bound for $$h^0(X,L)$$ h 0 ( X , L</mml:m...

We introduce the notion of a generalized semi-ideal in a ternary semiring. Various examples to establish a relationship between ideals, bi-ideals, quasi-ideals and generalized semi-ideals are furnished. A criterion for a commutative ternary semiring without any divisors of zero to a ternary division semiring is given. AMS Mathematics Subject Classification (2010): 16Y60, 16Y99

The aim of this paper is to introduce and study the notions of  (resp., pre, semi, )-open sets in terms of an ideal I. These concepts generalize the usual notions of  (resp., pre, semi, ) open sets. Also, several of their topological properties are investigated.

The paper introduces a new generalized closed set via semi local function. Its relationship with other existing generalized closed sets are established. It’s basic properties are discussed. A new decomposition of continuity is derived. General Terms Ideal topological space, local function and semi-local function.

A toric face ring, which generalizes both Stanley-Reisner rings and affine semigroup rings, is studied by Bruns, Römer and their coauthors recently. In this paper, under the “normality” assumption, we describe a dualizing complex of a toric face ring R in a very concise way. Since R is not a graded ring in general, the proof is not straightforward. We also develop the squarefree module theory o...

We give a new proof of Kollár’s conjecture on the derived pushforward dualizing sheaf twisted by variation Hodge structure. This has been settled M. Saito via theory mixed modules and various applications in investigation Albanese maps. Our technique is $$L^2$$ theoretic which gives concrete constructions proofs to conjecture. The point view allows us generalize context non-abelian theory.

We study presentations of the virtual dualizing modules special linear groups number rings, Steinberg modules. Bykovskii gave a presentation for integers, and our main result is generalization this to Gaussian integers Eisenstein integers. also show that does not give several Euclidean rings.