Hypersurfaces

The interplay between geometry and topology on complex algebraic varieties is a classical theme that goes back to Lefschetz [L] and Zariski [Z] and is always present on the scene; see for instance the work by Libgober [Li]. In this paper we study complements of hypersurfaces, with special attention to the case of hyperplane arrangements as discussed in OrlikTerao’s book [OT1]. Theorem 1 expresses the degree of the gradient map associated to any homogeneous polynomial h as the number of ncells that have to be added to a generic hyperplane section D(h) ∩ H to obtain the complement in...
36p tuanloccuoi 04012013 124 5 Download

Let M be an isoparametric hypersurface in the sphere S n with four distinct principal curvatures. M¨nzner showed that the four principal curvatures can u have at most two distinct multiplicities m1 , m2 , and Stolz showed that the pair (m1 , m2 ) must either be (2, 2), (4, 5), or be equal to the multiplicities of an isoparametric hypersurface of FKMtype, constructed by Ferus, Karcher and M¨nzner from orthogonal representations of Cliﬀord algebras. In this paper, u we prove that if the multiplicities satisfy m2 ≥ 2m1 − 1, then the isoparametric hypersurface M must be...
77p noel_noel 17012013 37 5 Download

The aim of this paper is to show that the preservation of irreducibility of sections between a variety and hypersurface by specializations and almost all sections between a linear subspace of dimension h = n − d of Pn and a nondegenerate variety k of dimension d 0 consists of s points in uniform position. Introduction The lemma of Haaris [2] about a set in the uniform position has attracted much attention in algebraic geometry. That is a set of points of a projective space such that any two subsets of them with the same cardinality have the same...
9p tuanlocmuido 19122012 34 2 Download

This paper deals with the relative nullity distributions of lightlike hypersurfaces of indefinite Kenmotsu space forms, tangent to the structure vector field. Theorems on parallel vector fields are obtained. We give characterization theorems for the relative nullity distributions as well as for Einstein, totally contact umbilical and flat lightlike hypersurfaces.
21p tuongvidanh 06012019 15 0 Download

We mainly deal with the problem of admissibility for screen distributions on a lightlike hypersurface of both a semiRiemannian manifold and an indefinite S manifold. In the latter case, we first show that a characteristic screen distribution is never admissible, and then we provide a characterization for admissible screen distributions on proper totally umbilical lightlike hypersurfaces.
13p tuongvidanh 06012019 12 0 Download

We study lightlike hypersurfaces of a semiRiemannian manifold satisfying pseudosymmetry conditions. We give sufficient conditions for a lightlike hypersurface to be pseudosymmetric and show that there is a close relationship of the pseudosymmetry condition of a lightlike hypersurface and its integrable screen distribution.
21p danhdanh27 07012019 8 0 Download

We prove the nonexistence of Hopf real hypersurfaces in complex twoplane Grassmannians whose shape operator A is generalized Tanaka–Webster recurrent if the principal curvature of the structure vector field is not equal to trace(A).
9p danhdanh27 07012019 7 0 Download

We define the notion of a metallic shaped hypersurface and give the full classification of metallic shaped hypersurfaces in real space forms. We deduce that every metallic shaped hypersurface in real space forms is a semisymmetric hypersurface.
11p danhdanh27 07012019 10 0 Download

In this paper, we investigate lightlike hypersurfaces which are semisymmetric, Ricci semisymmetric, parallel or semiparallel in a semiEuclidean space. We obtain that every screen conformal lightlike hypersurface of the Minkowski spacetime is semisymmetric.
24p danhdanh27 07012019 11 0 Download

In this paper, lightlike hypersurfaces of indefinite Kenmotsu space form are studied. Some characterizations of nonexistence of lightlike hypersurfaces of indefinite Kenmotsu space form are given.
13p danhdanh27 07012019 6 0 Download

In this article, we prove a uniqueness theorem for algebraically nondegenerate holomorphic curves on annulus sharing hypersurfaces in general position for Veronese embedding.
7p vimessi2711 02042019 7 0 Download

The purpose of this article is to show that there exists a smooth real hypersurface germ (M p), of D'Angelo infinite type in C2 such that it does not admit any (singular) holomorphic curve that has infinite order contact with M at p .
6p viposeidon2711 17092019 10 0 Download

In this paper, we establish a second main theorem with a good defect relation for entire curves in a projective variety whose derivatives vanish on inverse image of hypersurface targets. Our method is a combination of the techniques in [79].
10p koxih_kothogmih5 04092020 5 0 Download

In this paper we give a new proof for the classiﬁcation result in [3]. We show that isoparametric hypersurfaces with four distinct principal curvatures in spheres are of Cliﬀord type provided that the multiplicities m1 , m2 of the principal curvatures satisfy m2 ≥ 2m1 − 1. This inequality is satisﬁed for all but ﬁve possible pairs (m1 , m2 ) with m1 ≤ m2 .
15p dontetvui 17012013 56 6 Download

A uniqueness theorem for meromorphic mappings with hypersurfaces and without counting multiplicities
In 1926, R. Nevanlinna [6] showed that for two nonconstant meromorphic functions f and g on the complex plane C , if they have the same inverse images for five distinct values then f=g. In 1975, H. Fujimoto [4] generalized the above result to the case of meromorphic mappings of m C into n.
4p cumeo2006 02072018 11 1 Download

In this paper, by applying the generalized Omori–Yau maximum principle for complete spacelike hypersurfaces in warped product spaces, we obtain the sign relationship between the derivative of warping function and support function.
12p danhdanh27 07012019 4 0 Download

Classical differential geometry is the approach to geometry that takes full advantage of the introduction of numerical coordinates into a geometric space. This use of coordinates in geometry was the essential insight of Rene Descartes that allowed the invention of analytic geometry and paved the way for modern differential geometry. The basic object in differential geometry (and differential topology) is the smooth manifold. This is a topological space on which a sufficiently nice family of coordinate systems or "charts" is defined.
0p taurus23 26092012 71 9 Download

We prove Maruyama’s conjecture on the boundedness of slope semistable sheaves on a projective variety deﬁned over a noetherian ring. Our approach also gives a new proof of the boundedness for varieties deﬁned over a characteristic zero ﬁeld. This result implies that in mixed characteristic the moduli spaces of Gieseker semistable sheaves are projective schemes of ﬁnite type. The proof uses a new inequality bounding slopes of the restriction of a sheaf to a hypersurface in terms of its slope and the discriminant.
27p tuanloccuoi 04012013 44 6 Download

Let X be a smooth quasiprojective subscheme of Pn of dimension m ≥ 0 over Fq . Then there exist homogeneous polynomials f over Fq for which the intersection of X and the hypersurface f = 0 is smooth. In fact, the set of such f has a positive density, equal to ζX (m + 1)−1 , where ζX (s) = ZX (q −s ) is the zeta function of X. An analogue for regular quasiprojective schemes over Z is proved, assuming the abc conjecture and another conjecture. 1. Introduction The classical Bertini theorems say that if a subscheme...
30p tuanloccuoi 04012013 40 6 Download

In this paper, we develop an approach for establishing in some important cases, a conjecture made by De Giorgi more than 20 years ago. The problem originates in the theory of phase transition and is so closely connected to the theory of minimal hypersurfaces that it is sometimes referred to as “the version of Bernstein’s problem for minimal graphs”. The conjecture has been completely settled in dimension 2 by the authors [15] and in dimension 3 in [2], yet the approach in this paper seems to be the ﬁrst to use, in an essential way, the solution of...
23p tuanloccuoi 04012013 53 4 Download