Related papers: Versality in mirror symmetry
In this note, we explain how mirror symmetry for basic local models in the Gross-Siebert program can be understood through the non-toric blowup construction described by Gross-Hacking-Keel. This is part of a program to understand the…
This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different)…
This paper studies the problem of identifying directions of axial symmetry in multivariate distributions. Theoretical results are derived on how the measure or cardinality of the set of symmetry directions relates to spherical symmetry. The…
This paper explores homological mirror symmetry for weighted blowups of toric varieties. It will be shown that both the A-model and B-model categories have natural semiorthogonal decompositions. An explicit equivalence of the right…
Symmetric non-expanding horizons are studied in arbitrary dimension. The global properties -as the zeros of infinitesimal symmetries- are analyzed particularly carefully. For the class of NEH geometries admitting helical symmetry a…
We identify a certain universal Landau-Ginzburg model as a mirror of the big equivariant quantum cohomology of a (not necessarily compact or semipositive) toric manifold. The mirror map and the primitive form are constructed via Seidel…
In mirror symmetry, after the work by J. Walcher, the number of holomorphic disks with boundary on the real quintic lagrangian in a general quintic threefold is related to the periods of the mirror quintic family with boundary on two…
We introduce a consistent estimator for the homology (an algebraic structure representing connected components and cycles) of level sets of both density and regression functions. Our method is based on kernel estimation. We apply this…
It is argued that every Calabi-Yau manifold $X$ with a mirror $Y$ admits a family of supersymmetric toroidal 3-cycles. Moreover the moduli space of such cycles together with their flat connections is precisely the space $Y$. The mirror…
We generalize a recent result by J.F. Carlson to finite tensor categories having finitely generated cohomology. Specifically, we show that if the Krull dimension of the cohomology ring is sufficiently large, then there exist infinitely many…
We introduce a new homology theory of quandles, called simplicial quandle homology, which is quite different from quandle homology developed by Carter et al. We construct a homomorphism from a quandle homology group to a simplicial quandle…
The notion of hidden symmetry algebra used in the context of exactly solvable systems is re-examined from the purely algebraic way, analyzing subspaces of commuting polynomials that generate finite-dimensional quadratic algebras. By…
When string theory is compactified on a six-dimensional manifold with a nontrivial NS flux turned on, mirror symmetry exchanges the flux with a purely geometrical composite NS form associated with lack of integrability of the complex…
In the paper the main attention is paid to conditions on algebras from a given variety which provide coincidence of their algebraic geometries. The main part here play the notions mentioned in the title of the paper.
This expository article discusses recent advances in understanding 3-dimensional mirror symmetry and the mathematical definitions of the Higgs and Coulomb branches. This is a slightly expanded version of an article appearing in the Notices…
We generalize Friedman's notion of d-semistability, which is a necessary condition for spaces with normal crossings to admit smoothings with regular total space. Our generalization deals with spaces that locally look like the boundary…
The general concept of symmetry is realized in manifold ways in different realms of reality, such as plants, animals, minerals, mathematical objects or human artefacts in literature, fine arts and society. In order to arrive at a common…
An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…
Our objective in this article is to show a possibly interesting structure of homotopic nature appearing in persistent (co)homology. Assuming that the filtration of the (say) simplicial set embedded in a finite dimensional vector space…
This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection…