Related papers: On vanishing theorems for analytic spaces
We construct Morse homology groups associated with any regular function on a smooth complex algebraic variety, allowing singular and non-compact critical loci. These groups are generated by critical points of a certain large pertubation of…
In this work we generalize the classical notion of a (compact) twistor line in the period domain of compact complex tori. We introduce two new types of lines, which are non-compact analytic curves in the period domain of complex tori. We…
Let $A$ denote an affine algebra over an algebraically closed field $k$, with $\dim A=d\geq 3$. In the light of availability of cancellation theorems for stably free modules $P$ with $rank(P)=d-1$ (corank one), we try to implement the…
The aim of this paper is to present a survey of some recent results obtained in the study of spaces with asymmetric norm. The presentation follows the ideas from the theory of normed spaces (topology, continuous linear operators, continuous…
We present a setting for the study of torsion theories in general categories. The idea is to associate, with any pair ($\mathcal T$, $\mathcal F$) of full replete subcategories in a category $\mathcal C$, the corresponding full subcategory…
Spaces of quasi-analytic classes are defined by the existence and uniqueness of Taylor expansions, which are not necessarily convergent. First examples were given by Borel in his theory of monogenic functions, a generalisation of…
We consider a generalization of the axioms of a TQFT, so called half-projective TQFT's, with an anomaly, $x^{\mu}$, in the composition law. $\mu$ is a coboundary on the cobordism categories with non-negative, integer values. The element $x$…
We study torsors for groups defined by algebraic difference equations. Our main result provides necessary and sufficient conditions on the base difference field for all such torsors to be trivial. We also present an application to the…
Let X be a (connected and reduced) complex space. A q-collar of X is a bounded domain whose boundary is a union of a strongly q-pseudoconvex, a strongly q-pseudoncave and two flat (i.e. locally zero sets of pluriharmonic functions)…
In recent years, discrete spaces such as graphs attract much attention as models for physical spacetime or as models for testing the spirit of non-commutative geometry. In this work, we construct the differential algebras for graphs by…
We prove a vanishing theorem for the twisted de Rham cohomology of a compact manifold.
These are notes from my lectures on quantum K-theory of Nakajima quiver varieties and K-theoretic Donaldson-Thomas theory of threefolds given at Columbia and Park City Mathematics Institute. They contain an introduction to the subject and a…
We define analytic torsion of Z_2-graded elliptic complexes as an element in the graded determinant line of the cohomology of the complex, generalizing most of the variants of Ray-Singer analytic torsion in the literature. It applies to a…
A differential form vanishing on the tangent space at smooth points of a reduced embedded analytic germ is called conormal. For proving that a conormal one--form of a hypersurface vanishes at its singularities we state a Bertini--type…
Given a smooth projective variety over a perfect field of positive characteristic, we prove that the higher cohomologies vanish for the tensor product of the Witt canonical sheaf and the Teichmuller lift of an ample invertible sheaf. We…
In this paper, we establish several results related to vanishing theorems for Mather-Jacobian multiplier ideals on a Gorenstein projective variety, including an injectivity theorem, a Nadel-type vanishing theorem, a Griffith-type vanishing…
In this paper, we systematically apply Grothendieck duality theorem to simplify the proofs of several theorems in different papers: Including a vanishing theorem in KMM, a theorem of Koll\'{a}r's paper, a vanishing theorem due to Kov\'{a}cs…
This paper surveys Campana's theory of C-pairs (or "geometric orbifolds") in the complex-analytic setting, to serve as a reference for future work. Written with a view towards applications in hyperbolicity, rational points, and entire…
The dimension of any module over an algebra of affiliated operators ${\mathcal U}$ of a finite von Neumann algebra ${\mathcal A}$ is defined using a trace on ${\mathcal A}.$ All zero-dimensional ${\mathcal U}$-modules constitute the torsion…
This paper includes new bounds concepting the vanishing generalized weighted Morrey space. In this sense, it is outlined improved bounds about the a class of fractional type rough higher order commutators on vanishing generalized weighted…