Book contents
- Frontmatter
- Foreword
- List of Contributors
- Contents
- Introduction (by K. Ueno and T. Shioda)
- Part I
- Part II
- Complex Structures on S2p+1 × S2q+1 with Algebraic Codimension 1
- Defining Equations for Certain Types of Polarized Varieties
- On Logarithmic Kodaira Dimension of Algebraic Varieties
- On a Characterization of Submanifolds of Hopf Manifolds
- Relative Compactification of the Néron Model and its Application
- Toroidal Degeneration of Abelian Varieties
- Kodaira Dimensions of Complements of Divisors
- Compact Quotients of C3 by Affine Transformation Groups, II
- Kodaira Dimensions for Certain Fibre Spaces
- Part III
- Index
Relative Compactification of the Néron Model and its Application
Published online by Cambridge University Press: 03 May 2010
- Frontmatter
- Foreword
- List of Contributors
- Contents
- Introduction (by K. Ueno and T. Shioda)
- Part I
- Part II
- Complex Structures on S2p+1 × S2q+1 with Algebraic Codimension 1
- Defining Equations for Certain Types of Polarized Varieties
- On Logarithmic Kodaira Dimension of Algebraic Varieties
- On a Characterization of Submanifolds of Hopf Manifolds
- Relative Compactification of the Néron Model and its Application
- Toroidal Degeneration of Abelian Varieties
- Kodaira Dimensions of Complements of Divisors
- Compact Quotients of C3 by Affine Transformation Groups, II
- Kodaira Dimensions for Certain Fibre Spaces
- Part III
- Index
Summary
Introduction
In this article we shall define an analytic Néron model, i.e., an analytic counterpart of Néron's minimal model [11], and prove the minimality of it among principal homogeneous spaces (§ 2, 3). This portion deals with a partial generalization of the notion of analytic fiber system of groups and related results in [4].
Secondly we shall relatively compactify an analytic Néron model by applying the theory of torus embeddings [3], [5]. One should recall that the usefulness of a relative compactification of Néron model has been conjectured in [11]. The original construction in [6] was given in a slightly different, elementary, however rather complicated form. To facilitate better understanding, we employ here the notations of torus embeddings.
Kodaira has made a deep investigation of elliptic fibrations of surfaces [4]. Iitaka [2] and Ogg [12] gave a numerical classification of singular fibers in a pencil of curves of genus two. Namikawa and Ueno [8], [9] gave their complete classification and made a systematic study of them, following in principle Kodaira. The final objective of this article is to construct a family of reduced singular fibers of genus two in a systematic and geometric way by making use of a relative compactification of the Neron model (§ 5, 6, 7). In this respect, the present article should be viewed as a continuation of [9], which its authors had intended to write at that time.
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- Information
- Complex Analysis and Algebraic GeometryA Collection of Papers Dedicated to K. Kodaira, pp. 207 - 226Publisher: Cambridge University PressPrint publication year: 1977
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