Related papers: On smooth Gorenstein polytopes
We construct new complete cotorsion pairs in the categories of modules and chain complexes over a Gorenstein ring $R$, from the notions of Gorenstein homological dimensions, in order to obtain new Abelian model structures on both…
Though much is known about ${\bf s}$-lecture hall polytopes, there are still many unanswered questions. In this paper, we show that ${\bf s}$-lecture hall polytopes satisfy the integer decomposition property (IDP) in the case of monotonic…
For a d-dimensional convex lattice polytope P, a formula for the boundary volume is derived in terms of the number of boundary lattice points on the first $\floor{d/2}$ dilations of P. As an application we give a necessary and sufficient…
The aim of this note is to take benefit of the foam nature of the Khovanov-Kuperberg algebras to compute the Grothendieck groups of their categories of finitely generated projective modules. The computation relies on the Hattori-Stallings…
In this paper, we exhibit a formula relating punctured Gromov-Witten invariants used by Gross and Siebert to 2-point relative/logarithmic Gromov-Witten invariants with one point-constraint for any smooth log Calabi-Yau pair $(W,D)$. Denote…
Unlike the Gorenstein projective and injective dimensions, the majority of results on the Gorenstein flat dimension have been established only over Noetherian (or coherent) rings. Naturally, one would like to generalize these results to any…
The Doran-Harder-Thompson "gluing/splitting" conjecture unifies mirror symmetry conjectures for Calabi-Yau and Fano varieties, relating fibration structures on Calabi-Yau varieties to the existence of certain types of degenerations on their…
The notion of polyptych lattices, introduced by Escobar, Harada, and Manon, wraps the data of a collection of lattices related by piecewise-linear bijections together into a single semi-algebraic object, equipped with its own notions of…
We consider the problem of interpolating functions partially defined over a distributive lattice, by means of lattice polynomial functions. Goodstein's theorem solves a particular instance of this interpolation problem on a distributive…
We study threefolds fibred by K3 surfaces admitting a lattice polarization by a certain class of rank 19 lattices. We begin by showing that any family of such K3 surfaces is completely determined by a map from the base of the family to the…
After giving a short introduction on smooth lattice polytopes, I will present a proof for the finiteness of smooth lattice polytopes with few lattice points. The argument is then turned into an algorithm for the classification of smooth…
In this paper, we first study the Gorenstein projective/flat dimension of complexes of modules. The relation between the Gorenstein projective/flat dimension for complexes and that for modules are investigated. Then we study Tate, stable…
Let $\mathcal{X}$ be a class of left $R$-modules, $\mathcal{Y}$ be a class of right $R$-modules. In this paper, we introduce and study Gorenstein $(\mathcal{X}, \mathcal{Y})$-flat modules as a common generalization of some known modules…
Consider a log Calabi-Yau pair $(X,D)$ consisting of a smooth del Pezzo surface $X$ of degree $\geq 3$ and a smooth anticanonical divisor $D$. We prove a correspondence between genus zero logarithmic Gromov-Witten invariants of $X$…
The stability of the class of projectively coresolved Gorenstein flat modules, under the very Gorenstein process used to define them, is proven in this paper. Moreover, a new characterization of the projectively coresolved Gorenstein flat…
The splitting of a high-order optical vortex into a constellation of unit vortices, upon total reflection, is described and analyzed. The vortex constellation generalizes, in a local sense, the familiar longitudinal Goos-H\"anchen and…
We develop some ideas of Morrison and Plesser and formulate a precise mathematical conjecture which has close relations to toric mirror symmetry. Our conjecture, we call it Toric Residue Mirror Conjecture, claims that the generating…
We construct a surprisingly large class of new Calabi-Yau 3-folds $X$ with small Picard numbers and propose a construction of their mirrors $X^*$ using smoothings of toric hypersurfaces with conifold singularities. These new examples are…
Let $T_R(M)$ be a tensor ring, where $R$ is a ring and $M$ is an $N$-nilpotent $R$-bimodule. Under certain conditions, we characterize the Gorenstein flat-cotorsion modules over $T_R(M)$, showing that a $T_R(M)$-module $(X, u)$ is…
Brane tilings are bipartite periodic graphs on the 2-torus and realize a large family of 4d N=1 supersymmetric gauge theories corresponding to toric Calabi-Yau 3-folds. We present a complete classification of dimer integrable systems…