Related papers: Toroidal crossings and logarithmic structures

We develop the technique of weight truncation in the context of wall-crossings in birational cobordisms, parallel to that in [HL15, BFK19]. More precisely, for each such wall-crossing, we embed the bounded above derived category of coherent…

In this paper we study dually flat spaces arising from Delzant polytopes equipped with a symplectic potential together with their corresponding toric K\"ahler manifolds as their torifications.We introduce a dually flat structure and the…

We develop an approach to study the irreducibility of generic complete intersections in the algebraic torus defined by equations with fixed monomials and fixed linear relations on coefficients. Using our approach we generalize the…

This paper is devoted to systematically extend $f$-mirror symmetry between families of hypersurfaces in complete toric varieties, as introduced in \cite{R-fTV}, to families of complete intersections subvarieties. Namely, $f$-mirror symmetry…

For each family of Calabi-Yau hypersurfaces in toric varieties, Batyrev has proposed a possible mirror partner (which is also a family of Calabi-Yau hypersurfaces). We explain a natural construction of the isomorphism between certain Hodge…

We consider the concept of a generalised manifold in the O(d,d) setting, i.e., in double geometry. The conjecture by Hohm and Zwiebach for the form of finite generalised diffeomorphisms is shown to hold. Transition functions on overlaps are…

In this paper, we propose a new way to approach qudit systems using toric geometry and related topics including the local mirror symmetry used in the string theory compactification. We refer to such systems as (n,d) quantum systems where…

We introduce a formalism for handling general spaces of hierarchical tilings, a category that includes substitution tilings, Bratteli-Vershik systems, S-adic transformations, and multi-dimensional cut-and-stack transformations. We explore…

The purpose of this paper is to review some combinatorial ideas behind the mirror symmetry for Calabi-Yau hypersurfaces and complete intersections in Gorenstein toric Fano varieties. We suggest as a basic combinatorial object the notion of…

Topological semimetals can be classified by the connectivity and dimensionality of the band cross- ing in momentum space. The band crossings of a Dirac, Weyl, or an unconventional fermion semimet- al are 0D points, whereas the band…

Recent work ([18], [1]) has produced a complete list of weighted homogeneous surface singularities admitting smoothings whose Milnor fibre has only trivial rational homology (a "rational homology disk"). Though these special singularities…

We generalize the intersection theory of nef toric (Weil) b-divisors on smooth and complete toric varieties to the case of smooth and complete toroidal embeddings. As a key ingredient we show the existence of a limit measure, supported on…

Pulling back complex structures along a branched covering induces a holomorphic isometric embedding of Teichm\"uller spaces. We show that for dimension at least $2$, all isometric embeddings arise from branched coverings. This generalizes a…

Given an abelian category and a stability condition satisfying appropriate conditions, we define generalized $K$-theoretic invariants and prove that they satisfy wall-crossing formulas. For this, we introduce a new associative algebra…

We construct relative Gromov--Witten theory with expanded degenerations in the normal crossings setting and establish a degeneration formula for the resulting invariants. Given a simple normal crossings pair $(X,D)$, we show that there…

A growing body of evidence suggests that the complexity of Feynman integrals is best understood through geometry. Recent mathematical developments [Kontsevich and Soibelman, arXiv:2402.07343] have illuminated the role of exponential…

We investigate some general machinery for describing semidualizing modules over generic constructions like ladder determinantal rings with coefficients in a normal domain. We also pose and investigate natural localization questions that…

The subject is partial resolution of singularities. Given an algebraic variety X (not necessarily equidimensional) in characteristic zero (or, more generally, a pair (X,D), where D is a divisor on X), we construct a functorial…

We explicitly construct a $V$-normal crossing Gorenstein canonical model of the relative symmetric products of a local semistable degeneration of surfaces without a triple point by means of toric geometry. Using this model, we calculate the…

Given an effective action of an (n-1)-dimensional torus on an n-dimensional normal affine variety, Mumford constructs a toroidal embedding, while Altmann and Hausen give a description in terms of a polyhedral divisor on a curve. We compare…