Hypersurfaces

Mục đích của bài luận văn là nghiên cứu một số tính chất của lớp các hàm số triệt tiêu cấp vô hạn và ứng dụng của chúng trong bài toán về sự tồn tại trường vectơ chỉnh hình tiếp xúc. Luận văn trình bày lại một số kết quả trong bài báo “A note on uniqueness boundary of holomorphic mappings” của các tác giả Ninh Văn Thu, Nguyễn Ngọc Khanh và tiền ấn phẩm “On the nonexistence of nontrivial tangential holomorphic vector fields of a certain hypersurface of infinite type” của tác giả Ninh Văn Thu.

28p capheviahe26 02-02-2021 24 2   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 17-01-2013 64 7   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 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...

77p noel_noel 17-01-2013 46 7   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 04-01-2013 47 7   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 04-01-2013 49 8   Download

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...

36p tuanloccuoi 04-01-2013 228 8   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 04-01-2013 58 5   Download