Homogeneous polynomials

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 52 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 246 8   Download

SOLVABILITY CONDITIONS FOR SOME DIFFERENCE OPERATORS N. C. APREUTESEI AND V. A. VOLPERT Received 24 June 2004 Infinite-dimensional difference operators are studied. Under the assumption that the coefficients of the operator have limits at infinity, limiting operators and associated polynomials are introduced. Under some specific conditions on the polynomials, the operator is Fredholm and has the zero index. Solvability conditions are obtained and the exponential behavior of solutions of the homogeneous equation at infinity is proved. 1.

13p sting12 10-03-2012 37 5   Download

Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: Van der Waerden/Schrijver-Valiant like Conjectures and Stable (aka Hyperbolic) Homogeneous Polynomials: One Theorem for all...

26p thulanh6 15-09-2011 47 4   Download

Chúng tôi cung cấp cho một cuộc khảo sát ngắn gọn trên một phương pháp tiếp cận mới trong nghiên cứu của máy chiếu đa thức bảo toàn đồng nhất một phần phương trình vi phân hoặc quan hệ khác biệt giữa đồng nhất, và các tài sản của họ suy về không gian của điều kiện suy.

14p phalinh21 01-09-2011 63 4   Download