Hypersurfaces

Xem 1-10 trên 10 kết quả 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 Orlik-Terao’s book [OT1]. Theorem 1 expresses the degree of the gradient map associated to any homogeneous polynomial h as the number of n-cells that have to be added to a generic hyperplane section D(h) ∩ H to obtain the complement in...

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  • 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 FKM-type, 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...

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  • 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...

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  • 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 .

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  • 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.

    pdf0p taurus23 26-09-2012 30 6   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.

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  • 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...

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  • 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...

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  • Sự tiến hóa của một di chuyển hypersurface theo độ cong trung bình của nó đã được xem xét bởi Brakke [1] theo quan điểm hình học của, và bởi Evans, Spruck [3] theo điểm analysic. Bắt đầu từ một Γ0 bề mặt ban đầu trong R n, các bề mặt

    pdf10p phalinh19 22-08-2011 11 1   Download

  • In conclusion, let us outline a different argument, very much in the spirit of Lectures 8 and 5. We considered in these lectures the space of polynomials of a certain type (such as x3 + px + q or x5 − x + a) and saw that the set of polynomials with multiple roots separated the whole space into pieces, corresponding to the number of roots of a polynomial. The set of polynomials with multiple roots is a (very singular) hypersurface obtained by equating the discriminant of a polynomial to zero.

    pdf583p dacotaikhoan 25-04-2013 26 1   Download

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