相关论文: Semi-parallel real hypersurfaces in complex two-pl…
We derive a combinatorial sufficient condition for a partial correlation hypersurface in the parameter space of a directed Gaussian graphical model to be nonsingular, and speculate on whether this condition can be used in algorithms for…
The relationship between interpolation and separation properties of hypersurfaces in Bargmann-Fock spaces over $\mathbb{C} ^n$ is not well-understood except for $n=1$. We present four examples of smooth affine algebraic hypersurfaces that…
We show that for a smooth hypersurface $X\subset \bbP^n$ of degree at least 2, there exist arithmetically Cohen-Macaulay (ACM) codimension two subvarieties $Y\subset X$ which are not an intersection $X\cap{S}$ for a codimension two…
In our previous works we have classified real non-singular cubic hypersurfaces in the 5-dimensional projective space up to equivalence that includes both real projective transformations and continuous variations of coefficients preserving…
We prove an invariance of plurigenera for some foliated surface pairs of general type.
In this paper we prove a desingularization theorem for Legendrian surfaces that are the conormal of a quasi-ordinary hypersurface.
We classify, up to isometric congruence, the homogeneous hypersurfaces in the Riemannian symmetric spaces $\mathrm{SL}(3,\mathbb{H})/\mathrm{Sp}(3), \hspace{1pt} \mathrm{SO}(5,\mathbb{C})/\mathrm{SO}(5),$ and…
In this paper we further develop a Grassmannian technique used to prove results about very general hypersurfaces and present three applications. First, we provide a short proof of the Kobayashi Conjecture given previous results on the…
To every projective variety $X$, we associate a family of hypersurfaces in different Grassmannians, called the coisotropic hypersurfaces of $X$. These include the Chow form and the Hurwitz form of $X$. Gel'fand, Kapranov and Zelevinsky…
We generalize the notion of coisotropic hypersurfaces to subvarieties of Grassmannians having arbitrary codimension. To every projective variety X, Gel'fand, Kapranov and Zelevinsky associate a series of coisotropic hypersurfaces in…
Explicit representations of complex structures on closed manifolds are valuable, but relatively rare in the literature. Using isoparametric theory, we construct complex structures on isoparametric hypersurfaces with $g=4, m=1$ in the unit…
We show there exists a closed graph manifold $N$ and infinitely many non-separable, horizontal surfaces $\{S_{n} \to N\}_{n \in \mathbb{N}}$ such that there does not exist a quasi-isometry $\pi_1(N) \to \pi_1(N)$ taking $\pi_1(S_{n})$ to…
We construct examples of complex algebraic surfaces not admitting normal embeddings (in the sense of semialgebraic or subanalytic sets) with image a complex algebraic surface.
In this paper, we study locally strongly convex affine hypersurfaces with vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of affine metric. As the main result, we classify such…
We study non-existence of non-constant regular maps from a partial flag variety $X=G/P$ to another partial flag variety $X'=G'/P'$ and prove that there does not exist any non-constant regular map from any partial non-complete flag variety…
Generalising an example by Girondo and Wolfart, we use finite group theory to construct Riemann surfaces admitting two or more regular dessins (i.e. orientably regular hypermaps) with automorphism groups of the same order, and in many cases…
There are examples of complete spacelike surfaces in the Lorentzian product $\mathbb{H}^2\times\mathbb{R}_1$ with constant Gaussian curvature $K\leq -1$. In this paper, we show that there exists no complete spacelike surface in…
We prove the existence of surface subgroups within any cocompact lattice $\Gamma$ in $\mathrm{SO}(2n,1)$ for $n\geq2$. This result addresses the cases missing from the work of Hamenst\"adt in 2015, who constructed surface subgroups in…
We will announce two theorems. The first theorem will classify all topological types of degenerate fibers appearing in one-parameter families of Riemann surfaces, in terms of ``pseudoperiodic'' surface homeomorphisms. The second theorem…
A new model, in terms of finite bipartite graphs, of the free pseudosemilattice is presented. This will then be used to obtain several results about the variety SPS of all strict pseudosemilattices: (i) an identity basis for SPS is found,…