Related papers: Classification of Codazzi and note on minimal hype…

Let $N_{g,n}$ be a genus $g$ compact non-orientable surface with $n$ boundaries. We explain about relations on the level $d$ mapping class group $\mathcal{M}_d(N_{g,0})$ of $N_{g,0}$ and the level $d$ principal congruence subgroup…

Object of investigation are almost hypercomplex manifolds with Hermitian-Norden metrics of the lowest dimension. The considered manifolds are constructed on 4-dimensional Lie groups. It is established a relation between the classes of a…

In this paper we study general rotational surfaces in the 4- dimensional Euclidean space E4 and give a characterization of flat general rotation surface with pointwise 1-type Gauss map. Also, we show that a non-planar flat general rotation…

We deal with Perazzo 3-folds in $\mathbb P^4$, i.e. hypersurfaces $X=V(f)\subset \mathbb P^4$ of degree $d$ defined by a homogeneous polynomial $f(x_0,x_1,x_2,u,v)=p_0(u,v)x_0+p_1(u,v)x_1+p_2(u,v)x_2+g(u,v)$, where $p_0,p_1,p_2$ are…

We classify the solvable subalgebras, semisimple subalgebras, and Levi decomposable subalgebras of $\mathfrak{so}(4,\mathbb{C})$, up to inner automorphism. By Levi's Theorem, this is a full classification of the subalgebras of…

For each g > 2 and h > 1, we explicitly construct (1) fiber sum indecomposable relatively minimal genus g Lefschetz fibrations over genus h surfaces whose monodromies lie in the Torelli group, (2) fiber sum indecomposable genus g surface…

This is a preliminary note on a family of minimal surfaces in the 3-sphere defined by a compatible fourth order equation. The minimal surfaces are geometrically characterized either by having a surface of revolution like induced metric, or…

We classify $N{=}1$ $d=4$ kinematical and aristotelian Lie superalgebras with spatial isotropy, but not necessarily parity nor time-reversal invariance. Employing a quaternionic formalism which makes rotational covariance manifest and…

The Noether-Lefschetz theorem asserts that any curve in a very general surface $X$ in $\mathbb P^3$ of degree $d \geq 4$ is a restriction of a surface in the ambient space, that is, the Picard number of $X$ is $1$. We proved previously that…

We classify all smooth Calabi-Yau threefolds of Picard number two that have a general hypersurface Cox ring.

In this article we study compact Riemann surfaces with a non-large group of automorphisms of maximal order; namely, compact Riemann surfaces of genus $g$ with a group of automorphisms of order $4g-4.$ Under the assumption that $g-1$ is…

We study the birational geometry of hypersurfaces in projective varieties of the form $\mathbf{P}^1\times Z$, where $Z$ satisfies mild assumptions. Building on recent results of Herrera--Laface--Ugaglia, we study their Cox rings (when…

In this paper we give Weierstrass-type representation formulas for the null curves and for the minimal Lorentz surfaces in the Minkowski 3-space $\mathbb R^3_1$ using real-valued functions. Applying the Weierstrass-type representations for…

We show that for certain arithmetic groups, geometrically finite subgroups are the intersection of finite index subgroups containing them. Examples are the Bianchi groups and the Seifert-Weber dodecahedral space. In particular, for…

In this article, we construct two one-parameter families of properly embedded minimal surfaces in a three-dimensional Lie group $\widetilde{E(2)}$, which is the universal covering of the group of rigid motions of Euclidean plane endowed…

Using geometric engineering method of 4D $\mathcal{N}=2$ quiver gauge theories and results on the classification of Kac-Moody (KM) algebras, we show on explicit examples that there exist three sectors of $\mathcal{N}=2$ infrared CFT$_{4}$s.…

A monoid hypersurface is an irreducible hypersurface of degree d which has a singular point of multiplicity d-1. Any monoid hypersurface admits a rational parameterization, hence is of potential interest in computer aided geometric design.…

The parameter coclass has been used successfully in the study of nilpotent algebraic objects of different kinds. In this paper a definition of coclass for nilpotent semigroups is introduced and semigroups of coclass 0, 1, and 2 are…

In this paper, we study biconservative hypersurfaces in the four dimensional Minkowski space $\mathbb E^4_1$. We give the complete explicit classification of biconservative hypersurfaces with diagonalizable shape operator in $\mathbb…

We prove that there is a unique $R$-equivalence class on every del Pezzo surface of degree $4$ defined over the Laurent field $K=k((t))$ in one variable over an algebraically closed field $k$ of characteristic not equal to $2$ or $5$. We…