Related papers: Varieties with Degenerate Gauss Maps with Multiple…
We study normed groupoids with dilations and their induced deformations.
We study Gauss maps of order $k$, associated to a projective variety $X$ embedded in projective space via a line bundle $L.$ We show that if $X$ is a smooth, complete complex variety and $L$ is a $k$-jet spanned line bundle on $X$, with…
In this article, we present semiorthogonal decompositions for twisted forms of grassmannians
We introduce a general framework to unify several variants of twisted topological $K$-theory. We focus on the role of finite dimensional real simple algebras with a product-preserving involution, showing that Grothendieck-Witt groups…
In this paper, we establish an innovative framework in logarithmic Hodge theory for toroidal varieties, introducing weighted toroidal structures and developing a systematic obstruction theory for Hodge classes. Building upon recent advances…
We study large uniform random maps with one face whose genus grows linearly with the number of edges. They can be seen as a model of discrete hyperbolic geometry. In the past, several of these hyperbolic geometric features have been…
We consider a generalized Riemann-Hurwitz formula as it may be applied to rational maps between projective varieties having an indeterminacy set and fold-like singularities. The case of a holomorphic branched covering map is recalled. Then…
In this paper, we introduce the degenerate zero-truncated Poisson random variables whose probability mass functions are a natural extension of the zero-truncated Poisson distributions, and investigate various properties of those random…
We prove the existence of defective secant varieties of three-factor and four-factor Segre-Veronese varieties embedded in certain multi-degree. These defective secant varieties were previously unknown and are of importance in the…
In this paper, we establish a second main theorem for holomorphic maps with finite growth index on complex discs intersecting arbitrary families of hypersurfaces (fixed and moving) in projective varieties, which gives an above bound of the…
We construct a new presentation of the twisted Yangian of type $D$ with a finite number of generators. By using this presentation, we propose a new definition of the twisted affine Yangian of type $D$.
The usual notion of set-convexity, valid in the classical Euclidean context, metamorphoses into several distinct convexity types in the more general Riemannian setting. By studying this phenomenon in reverse, we characterize complete…
We study deformations of complex projective varieties that are homotopically or homologically trivial. We formulate several conjectures and give some examples and partial answers.
Marked vertex diagrams provide a combinatorial way to represent knotted surfaces in $\mathbb{R}^4$; including virtual crossings allows for a theory of virtual knotted surfaces and virtual cobordisms. Biquandle counting invariants are…
Let $G$ be a linear connected complex reductive Lie group. The purpose of this paper is to give explicit symplectic isomorphisms from twisted cotangent bundles of the complex generalized flag varieties, whose transition functions are given…
We analyze the effect of twists on the electronic structure of configurations of infinite stacks of graphene layers. We focus on three different cases: an infinite stack where each layer is rotated with respect to the previous one by a…
The existence and construction of common invariant cones for families of real matrices is considered. The complete results are obtained for 2x2 matrices (with no additional restrictions) and for families of simultaneously diagonalizable…
In this paper we present new proofs of the Conway-Gordon-Sachs and Sachs Theorems on the linked cycles in graphs embedded in $\R^3$. We reduce these theorems to certain property of graphs mapped to the plane.
In this paper, we deal with plane curves with cusps. It is well known that there are various types of cusps. Among them, we investigate criteria for $(n, n+1)$ cusps with respect to several differential conditions and relations between…
Regular edge-colored graphs encode colored triangulations of pseudo-manifolds. Here we study families of edge-colored graphs built from a finite but arbitrary set of building blocks, which extend the notion of $p$-angulations to arbitrary…