Related papers: Wonderful models for toric arrangements

In order to provide a good categorical setting to the many different spaces of fields arising in the description of physical theories, a pedagogical introduction to the categorical notion of smooth sets is provided and some simple…

We initiate the study of model structures on (categories induced by) lattice posets, a subject we dub homotopical combinatorics. In the case of a finite total order $[n]$, we enumerate all model structures, exhibiting a rich combinatorial…

We study geometric structures on the complement of a toric mirror arrangement associated with a root system. Inspired by those special hypergeometric functions found by Heckman-Opdam, as well as the work of Couwenberg-Heckman-Looijenga on…

We have previously proposed a study of arrangements of small circles which also surround regions in the plane realized as the images of natural real algebraic maps yielding Morse-Bott functions by projections. Among studies of arrangements,…

We give a combinatorial model for the bounded derived category of graded modules over the dual numbers in terms of arcs on the integer line with a point at infinity. Using this model we describe the lattice of thick subcategories of the…

We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…

We give a general account of family algebras over a finitely presented linear operad, this operad together with its presentation naturally defining an algebraic structure on the set of parameters.

For zero-dimensional complete intersections with homogeneous ideal generators of equal degrees over an algebraically closed field of characteristic zero, we give a combinatorial proof of the smoothness of the corresponding catalecticant…

We describe limits of line bundles on nodal curves in terms of toric arrangements associated to Voronoi tilings of Euclidean spaces. These tilings encode information on the relationship between the possibly infinitely many limits, and…

We show how an object from the combinatorially geometric version of the analytical number theory, namely geometric continued fractions, appears in the classical smooth dynamics, namely in the problem on the topological classification of…

Associated to any hypergraph is a toric ideal encoding the algebraic relations among its edges. We study these ideals and the combinatorics of their minimal generators, and derive general degree bounds for both uniform and non-uniform…

We introduce topological notions of normal crossings symplectic divisor and variety and establish that they are equivalent, in a suitable sense, to the desired geometric notions. Our proposed concept of equivalence of associated topological…

A toric hyperplane is the preimage of a point $x \in S^1$ of a continuous surjective group homomorphism $\theta: \mathbb{T}^n \to S^1$. A finite hyperplane arrangement is a finite collection of such hyperplanes. In this paper, we study the…

Twist tori are examples of exotic monotone lagrangian tori, presented in [1]. This tree of examples grew up over the first one --- the torus $\Theta \in \R^4$, constructured in [2] and [3]. On the other hand, in [4] and [5] we proposed a…

We study the relative Hilbert scheme of a family of nodal (or smooth) curves, over a base of arbitrary dimension, via its (birational) cycle map, going to the relative symmetric product. We show the cycle map is the blowing up of the…

This paper develops a formal theory of musical scales and their harmonic coverings and introduces orbit covers: coverings obtained by translating a fixed subset across a scale via a group action. Orbit covers generalize familiar…

The fundamental group of the complement of a hyperplane arrangement plays an important role in studying the corresponding arrangements. In particular, for large families of hyperplane arrangements, this fundamental group, being isomorphic…

We introduce a new class of structured symmetric matrices by extending the notion of perfect elimination ordering from graphs to weighted graphs or matrices. This offers a common framework capturing common vertex elimination orderings of…

For line arrangements in P^2 with nice combinatorics (in particular, for those which are nodal away the line at infinity), we prove that the combinatorics contains the same information as the fundamental group together with the meridianal…

Toric geometry provides a bridge between the theory of polytopes and algebraic geometry: one can associate to each lattice polytope a polarized toric variety. In this thesis we explore this correspondence to classify smooth lattice…