Holomorphic mapping

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

The notions of hyperbolicity and tautness modulo an analytic subset of complex spaces are due to S. Kobayashi. Much attention has been given to these notions, and the results on this problem can be applied to many areas of mathematics, in particular to the extensions of holomorphic mappings. The main goal of this article is to give necessary and sufficient conditions on the hyperbolicity or tautness modulo an analytic subset of complex spaces.

10p tamynhan5 10-12-2020 12 2   Download

In this paper, we establish a second main theorem for holomorphic mappings from a disc (R) into Pn(C) and families of hyperplanes in subgeneral position. Our result is an extension the classical second main theorem of Cartan-Nochka and the second main theorem of Fujimoto.

9p tamynhan9 02-12-2020 10 3   Download

Given a holomorphic vector bundle E over a compact K¨hler manifold X, a one defines twisted Gromov-Witten invariants of X to be intersection numbers in moduli spaces of stable maps f : Σ → X with the cap product of the virtual fundamental class and a chosen multiplicative invertible characteristic class of the virtual vector bundle H 0 (Σ, f ∗ E) H 1 (Σ, f ∗ E). Using the formalism of quantized quadratic Hamiltonians [25], we express the descendant potential for the twisted theory in terms of that for X. ...

40p noel_noel 17-01-2013 57 7   Download

We prove that the classical Oka property of a complex manifold Y, concerning the existence and homotopy classification of holomorphic mappings from Stein manifolds to Y, is equivalent to a Runge approximation property for holomorphic maps from compact convex sets in Euclidean spaces to Y . Introduction Motivated by the seminal works of Oka [40] and Grauert ([24], [25], [26]) we say that a complex manifold Y enjoys the Oka property if for every Stein manifold X, every compact O(X)-convex subset K of X and every continuous map f0 : X → Y which is holomorphic in an...

20p noel_noel 17-01-2013 52 5   Download

In the symplectic category there is a ‘connect sum’ operation that glues symplectic manifolds by identifying neighborhoods of embedded codimension two submanifolds. This paper establishes a formula for the Gromov-Witten invariants of a symplectic sum Z = X#Y in terms of the relative GW invariants of X and Y . Several applications to enumerative geometry are given. Gromov-Witten invariants are counts of holomorphic maps into symplectic manifolds.

92p tuanloccuoi 04-01-2013 44 7   Download

The usual index theorems for holomorphic self-maps, like for instance the classical holomorphic Lefschetz theorem (see, e.g., [GH]), assume that the fixed-points set contains only isolated points. The aim of this paper, on the contrary, is to prove index theorems for holomorphic self-maps having a positive dimensional fixed-points set. The origin of our interest in this problem lies in holomorphic dynamics.

47p tuanloccuoi 04-01-2013 49 6   Download