Related papers: Injectivity Theorem for Generalised Pairs on Surfa…

In generalized complex geometry, we revisit linear subspaces and submanifolds that have an induced generalized complex structure. We give an expression of the induced structure that allows us to deduce a smoothness criteria, we dualize the…

Given a complex projective algebraic variety, write H(X) for its cohomology with complex coefficients and IH(X) for its Intersection cohomology. We first show that, under some fairly general conditions, the canonical map H(X)\to IH(X) is…

In this paper, we prove a theorem that gives a simple criterion for generating commuting pairs of generalized almost complex structures on spaces that are the product of two generalized almost contact metric spaces. We examine the…

We prove a general duality theorem for tangle-like dense objects in combinatorial structures such as graphs and matroids. This paper continues, and assumes familiarity with, the theory developed in [6]

In the study of homology cobordisms, knot concordance and link concordance, the following technical problem arises frequently: let $\pi$ be a group and let $M \to N$ be a homomorphism between projective $\Z[\pi]$-modules such that $\Z_p…

We establish the Kodaira vanishing theorem and the Kawamata-Viehweg vanishing theorem for lc generalized pairs. As a consequence, we provide a new proof of the base-point-freeness theorem for lc generalized pairs. This new approach allows…

The theory of frames normal for general connections on differentiable bundles is developed. Links with the existing theory of frames normal for covariant derivative operators (linear connections) in vector bundles are revealed. The…

In this article we show that a general notion of descent in coarse geometry can be applied to the study of injectivity of the $KH$-assembly map. We also show that the coarse assembly map is injective in general for finite coarse…

We prove a structure theorem for the Gromov-Witten invariants of compact Kahler surfaces with geometric genus $p_g>0$. Under the technical assumption that there is a canonical divisor that is a disjoint union of smooth components, the…

Let $(X,D)$ be a log-canonical (lc) pair, in which $X$ is a compact K\"ahler manifold and $D$ is a reduced snc divisor, and let $F$ be a holomorphic line bundle on $X$ equipped with a smooth metric $h_F = e^{-\varphi_F}$. Via the use of the…

We develop general theory of equivariant quantum cohomology for ample Kahler manifolds and prove the mirror conjecture for projective complete intersections.

We use Koll\'ar's gluing theory to prove the contraction theorem for generalized pairs. In particular, we show that we can run the MMP for any generalized log canonical pairs.

In this paper we introduce generalized symmetric Meir-Keeler contractions and prove some coupled fixed point theorems for mixed monotone operators $F:X \times X \rightarrow X$ in partially ordered metric spaces. The obtained results extend,…

We extend the assertion of the Generalized Lower Bound Theorem (GLBT) to general polytopes under the assumption that their low dimensional skeleton is simplicial, with partial results for the general case. We prove a quantitative version of…

In this paper, we prove the existence and conjugacy of injectors of a generalized $\pi$-soluble groups for the Hartley class defined by a invariable Hartley function, and give a description of the structure of the injectors.

We established a fixed-point theorem for mapping satisfying a general contractive inequality of integral type depended an another function. This theorem substantially extend the theorem due to Branciari (2003) and Rhoades (2003)

The purpose of this paper is to establish injectivity theorems for higher direct image sheaves of canonical bundles twisted by pseudo-effective line bundles and multiplier ideal sheaves. As applications, we generalize Koll'ar's torsion…

We note that the vanishing and injectivity theorems of Koll\'ar and Esnault-Viehweg can be used to give a quick algebraic proof of a strengthening of the Ein-Lazarsfeld Skoda-type division theorem for global sections of adjoint line bundles…

It is proved that for a Jacobi pair $(F,G)\in C[x,y]^2$, the Keller mapping: $(a,b)\mapsto(F(a,b),G(a,b))$ for $(a,b)\in C^2$, is injective. In particular, the $2$-dimensional Jacobi conjecture holds.

In this paper, we prove some common coupled fixed point theorems for mappings satisfying different contractive conditions in the context of complete $C^*$-algebra-valued metric spaces. Moreover, the paper provides an application to prove…