相关论文: Choking horns in Lipschitz Geometry of Complex Alg…
The purpose of this paper is to study algebras of singular integral operators on $\mathbb{R}^{n}$ and nilpotent Lie groups that arise when one considers the composition of Calder\'on-Zygmund operators with different homogeneities, such as…
Classification theory and the study of projective varieties which are covered by rational curves of minimal degrees naturally leads to the study of families of singular rational curves. Since families of arbitrarily singular curves are hard…
In this paper we study the bifurcations of a class of polycycles, called lips, occurring in generic three-parameter smooth families of vector fields on a M\"obius band. The lips consists of a set of polycycles formed by two saddle-nodes,…
Let $X$ be a closed algebraic subset of $\mathbb{A}^{n}(K)$ where $K$ is an algebraically closed field complete with respect to a nontrivial non-Archimedean valuation. We show that there is a surjective continuous map from the Berkovich…
We use tropical and nonarchimedean geometry to study the moduli space of genus $0$ stable maps to $\mathbb{P}^1$ relative to two points. This space is exhibited as a tropical compactification in a toric variety. Moreover, the fan of this…
We describe some families of differentiable vector fields with the Hopf bifurcation at infinity, without assuming the continuous differentiability. These vector fields have isolated singular points on the plane, and the initial families are…
A metrized complex of algebraic curves is a finite metric graph together with a collection of marked complete nonsingular algebraic curves, one for each vertex, the marked points being in bijection with incident edges. We establish a…
We construct a simple explicit local geometry providing a `bifid throat' for 5-brane axion monodromy. A bifid throat is a throat that splits into two daughter throats in the IR, containing a homologous 2-cycle family reaching down into each…
Symmetric homology is an analog of cyclic homology in which the cyclic groups are replaced by symmetric groups. The foundations for the theory of symmetric homology of algebras are developed in the context of crossed simplicial groups using…
It is shown that a bounded quiver algebra having a 2-truncated oriented cycle is of infinite Hochschild homology dimension and global dimension, which generalizes a result of Solotar and Vigu\'{e}-Poirrier to nonlocal ungraded algebras…
Inspired by the results obtained in \cite{SR}, in this work, we develop techniques to handle the contraction property for weak normalization and Lipschitz saturation of algebras for the following types of algebras: universally injective,…
A laycle is the categorical analogue of a lazy cocycle. Twines (as introduced by Bruguieres) and strong twines (as introduced by the authors) are laycles satisfying some extra conditions. If $c$ is a braiding, the double braiding $c^2$ is…
We study snarks whose edges cannot be covered by fewer than five perfect matchings. Esperet and Mazzuoccolo found an infinite family of such snarks, generalising an example provided by Hagglund. We construct another infinite family, arising…
We consider algebraic varieties canonically associated to any Lie superalgebra, and study them in detail for super-Poincar\'e algebras of physical interest. They are the locus of nilpotent elements in (the projectivized parity reversal of)…
A knot in the 3-sphere is called doubly slice if it is a slice of an unknotted 2-sphere in the 4-sphere. We give a bi-sequence of new obstructions for a knot being doubly slice. We construct it following the idea of Cochran-Orr-Teichner's…
We give new obstructions to the module structures arising in Heegaard Floer homology. As a corollary, we characterize the possible modules arising as the Heegaard Floer homology of an integer homology sphere with one-dimensional reduced…
A notion of a nearly toric variety is introduced. The examples of nearly toric varieties in the context of Schubert varieties are discussed. In particular, combinatorial characterizations of the smooth and singular nearly toric Schubert…
A conic bundle is a contraction $X\to Z$ between normal varieties of relative dimension $1$ such that $-K_X$ is relatively ample. We prove a conjecture of Shokurov which predicts that, if $X\to Z$ is a conic bundle such that $X$ has…
For the toric variety X associated to the Bruhat poset of Schubert varieties in the Grassmannian, we describe the singular locus in terms of the faces of the associated polyhedral cone. We also determine the tangent cones at the maximal…
We give a geometric interpretation of cluster varieties in terms of blowups of toric varieties. This enables us to provide, among other results, an elementary geometric proof of the Laurent phenomenon for cluster algebras (of geometric…