相关论文: Morphisms from Quintic Threefolds to Cubic Threefo…

There are six orientable, compact, flat 3-manifolds that can occur as cusp cross-sections of hyperbolic 4-manifolds. This paper provides criteria for exactly when a given commensurability class of arithmetic hyperbolic 4-manifolds contains…

We prove that every biregular automorphism of the affine algebraic variety ${\mathbb P}^M\setminus S$, $M\geqslant 3$, where $S\subset {\mathbb P}^M$ is a hypersurface of degree $m\geqslant M+1$ with a unique singular point of multiplicity…

Supersymmetry is considered in spaces of constant curvature (spherical, de Sitter and Anti-de Sitter spaces) of two, three and four dimensions.

We generalize recent results regarding the phase space of the mass deformed $E_1$ fixed point to a full class of five-dimensional superconformal field theories, known as $X_{1,N}$. As in the $E_1$ case, a phase transition occurs as a…

This article is a continuation of a previous article which concerned the splitting problem for subspaces of superspaces. We begin with a general account of projective superspaces. Subsequently, we specialise to subvarieties of `positive'…

We prove the existence of three irreducible curves $C_{12,m}$ of degree 12 with the same number of cusps and different Alexander polynomials. This exhibits a Zariski triple. Moreover we provide a set of generators for the elliptic threefold…

We study parameter spaces of linear series on projective curves in the presence of unibranch singularities, i.e. {\it cusps}; and to do so, we stratify cusps according to value semigroup. We show that {\it generalized Severi varieties} of…

We investigate proper biharmonic hypersurfaces with at most three distinct principal curvatures in space forms. We obtain the full classification of proper biharmonic hypersurfaces in 4-dimensional space forms.

A few facts concerning the phrase "the automorphism groups become larger at special points of the moduli of K3 surfaces" are presented. It is also shown that the automorphism groups are of infinite order over a dense subset in any…

Non-dicritical codimension one foliations on projective spaces of dimension four or higher always have an invariant algebraic hypersurface. The proof relies on a strengthening of a result by Rossi on the algebraization/continuation of…

A well-known conjecture asserts that smooth threefolds $X\subset\{\mathbb P}^5$ are quadratically normal with the only exception of the Palatini scroll. As a corollary of a more general statement we obtain the following result, which is…

This paper proves the following converse to a theorem of Mumford: Let $A$ be a principally polarized abelian variety of dimension five, whose theta divisor has a unique singular point, and suppose that the multiplicity of the singular point…

This article addresses the existence of $\Q$-rational periodic points for morphisms of projective space. In particular, we construct an infinitely family of morphisms on $\P^N$ where each component is a degree 2 homogeneous form in $N+1$…

A curve is called nondegenerate if it can be modeled by a Laurent polynomial that is nondegenerate with respect to its Newton polytope. We show that up to genus 4, every curve is nondegenerate. We also prove that the locus of nondegenerate…

Given a surface F, we are interested in Z/2 valued invariants of immersions of F into R^3, which are constant on each connected component of the complement of the quadruple point discriminant in Imm(F,R^3). Such invariants will be called…

Let k=F_q be a finite field of even characteristic. We obtain in this paper a complete classification, up to k-isomorphism, of non singular quartic plane curves defined over k. We find explicit rational normal models and we give closed…

We classify all possible automorphism groups of smooth cubic surfaces over an algebraically closed field of arbitrary characteristic. As an intermediate step we also classify automorphism groups of quartic del Pezzo surfaces. We show that…

We show that the dynamics of automorphisms on all projective complex manifolds X (of dimension 3, or of any dimension but assuming the Good Minimal Model Program or Mori's Program) are canonically built up from the dynamics on just three…

In this paper, we give a full classification of the separable hypersurfaces of constant sectional curvature in the Euclidean $n$-space $\mathbb{R}^n$. In dimension $n=3$, this classification was solved by Hasanis and L\'opez [Manuscripta…

Consider the smooth quadric Q_6 in P^7. The middle homology group H_6(Q_6,Z) is two-dimensional with a basis given by two classes of linear subspaces. We classify all threefolds of bidegree (1,p) inside Q_6.