Related papers: On a generalized canonical bundle formula and gene…
We generalize Demailly's construction of projective jet bundles and strictly negatively curved pseudometrics on them to the logarithmic case. We establish this logarithmic generalization explicitly via coordinates, just as Noguchi's…
We introduce the notion of a free associative $\mathcal{Z}_2$-algebra on the union of two disjoint sets and prove a generalization of Cohn's Theorem on Jordan algebras.
We use the canonical bundle formula for parabolic fibrations to give an inductive approach to the generalized abundance conjecture using nef reduction. In particular, we observe that generalized abundance holds for a klt pair $(X,B)$ if the…
We show that a weak version of the canonical bundle formula holds for fibrations of relative dimension one. We provide various applications thereof, for instance, using the recent result of Xu and Zhang, we prove the log non-vanishing…
Katzarkov has proposed a generalization of Kontsevich's mirror symmetry conjecture, covering some varieties of general type. We prove a version of this conjecture in the simplest example, relating the Fukaya category of a genus two curve to…
Generalized geometry finds many applications in the mathematical description of some aspects of string theory. In a nutshell, it explores various structures on a generalized tangent bundle associated to a given manifold. In particular,…
A generalization of Young's inequality for convolution with sharp constant is conjectured for scenarios where more than two functions are being convolved, and it is proven for certain parameter ranges. The conjecture would provide a unified…
Canonical extension has proven to be a powerful tool in algebraic study of propositional logics. In this paper we describe a generalization of the theory of canonical extension to the setting of first order logic. We define a notion of…
We discuss generalised duality theory for monoidal categories and its applications to the categories of exact endofunctors, graded vector spaces, and topological vector spaces.
We study tropical friezes and cluster-additive functions associated to symmetrizable generalized Cartan matrices in the framework of Fock-Goncharov duality in cluster algebras. In particular, we generalize and prove a conjecture of C. M.…
We study tropical friezes and cluster-additive functions associated to symmetrizable generalized Cartan matrices in the framework of Fock-Goncharov duality in cluster algebras. In particular, we generalize and prove a conjecture of C. M.…
We present generalized algebraic theories corresponding to slightly modified versions of two of the type theories in our paper Type Theory with Explicit Universe Polymorphism. We first present a generalized algebraic theory for categories…
We show that it is consistent, relative to the consistency of a strongly inaccessible cardinal, that an instance of the generalized Borel Conjecture introduced in [8] holds while the classical Borel Conjecture fails.
We prove a common extension of Bang's and Kadets' lemmas for contact pairs, in the spirit of the Colourful Carath\'eodory Theorem. We also formulate a generalized version of the affine plank problem and prove it under special assumptions.…
In this note, we generalize an ancient Greek inequality about the sequence of primes to the cases of arithmetic progressions even multivariable polynomials with integral coefficients. We also refine Bouniakowsky's conjecture [16] and…
Let S be a K3 surface and assume for simplicity that it does not contain any (-2)-curve. Using coherent systems, we express every non-simple Lazarsfeld-Mukai bundle on S as an extension of two sheaves of some special type, that we refer to…
We provide some necessary details to several arguments appearing in our previous paper ``Canonical bases for quantum generalized Kac-Moody algebras''. We also make the link with some other work on the same subject.
Several results about the union-closed sets conjecture are presented.
We review the concept of a graded bundle as a natural generalisation of a vector bundle. Such geometries are particularly nice examples of more general graded manifolds. With hindsight there are many examples of graded bundles that appear…
There are several extensions of the classical Banach Fixed Point Theorem in technical literature. A branch of generalizations replaces usual contractivity by weaker but still effective assumptions. Our note follows this stream, presenting…