Related papers: Applications of Kawamata's positivity theorem
In this paper we study relative Riemann-Zariski spaces attached to a morphism of schemes and generalizing the classical Riemann-Zariski space of a field. We prove that similarly to the classical RZ spaces, the relative ones can be described…
Simple argument in favour of unitarity, to all orders, of space-like noncommutative theory is given.
In this article an attempt is made to present very recent conceptual and computational developments in QFT as new manifestations of old and well establihed physical principles. The vehicle for converting the quantum-algebraic aspects of…
The quotient variety associated to a permutation representation of a finite group has only canonical singularities in arbitrary characteristic. Moreover, the log pair associated to such a representation is Kawamata log terminal except in…
We examine the dependence of quantization on global properties of a classical system. Quantization based on local properties may lead to ambiguities and inconsistency between local and global symmetries of a quantum system. Our quantization…
In this paper we give a construction for a special type of congruences on commutative semigroups. We apply our result for the multiplicative semigroup of all positive integers.
The definition of quantum singularity is extended from static space-times to conformally static space-times. After the usual definitions of classical and quantum singularities are reviewed, examples of quantum singularities in static…
I use an instrumental approach to investigate some commonly made claims about interpretations of quantum mechanics, especially those that pertain questions of locality. The here presented investigation builds on a recently proposed taxonomy…
We obtain restrictions on the rational homotopy types of mapping spaces and of classifying spaces of homotopy automorphisms by means of the theory of positive weight decompositions. The theory applies, in particular, to connected components…
We present a reduction of the function field Mordell-Lang conjecture to the function field Manin-Mumford conjecture, in all characteristics, via model theory, but avoiding recourse to the dichotomy theorems for (generalized) Zariski…
We observe that successive applications of known results from the theory of positive systems lead to an {\it efficient general algorithm} for positive realizations of transfer functions. We give two examples to illustrate the algorithm, one…
In this chapter, we will review the field-theoretic treatment of General Relativity based on an effective field theory extension of the Einstein-Hilbert action. This pragmatic route to low-energy quantum effects in gravity critically…
We establish the positive energy theorem for weak asymptotically anti-de Sitter initial data sets with distributional curvature under the weak dominant energy condition.
We develop the theory of Morrison-Kawamata dream spaces, which axiomatizes varieties (not necessarily of Calabi-Yau type) that satisfy the Morrison-Kawamata cone conjecture. Using this theory, we establish the generic deformation invariance…
In our previous work, a relation between Tsukiyama problem about self homotopy equivalence was found by using a generalization of phantom map. In this note, fundamental result is established for such a generalization. This is the first time…
Investigating quantum gravity requires a comprehension of both, general relativity and quantum field theory. Therefore this thesis starts, after a general introduction to the treated topics, with a brief review of the field theoretical…
The concepts of complementarity and entanglement are considered with respect to their significance in and beyond physics. A formally generalized, weak version of quantum theory, more general than ordinary quantum theory of material systems,…
Some quantum mechanical potentials, singular at short distances, lead to ultraviolet divergences when used in perturbation theory. Exactly as in quantum field theories, but much simpler, regularization and renormalization lead to finite…
We extend the theory of decomposable maps by giving a detailed description of k-positive maps. A relation between transposition and modular theory is established. The structure of positive maps in terms of modular theory (the generalized…
Based on a classical result on partitions of an integer into a finite set of positive integers, we establish a general positivity result on coefficients of certain $q$-series which uniformly refines the positivity of truncated pentagonal…