Algebraic Geometry and Commutative Algebra

Algebraic Geometry and Commutative Algebra in Honor of Masayoshi Nagata presents a collection of papers on algebraic geometry and commutative algebra in honor of Masayoshi Nagata for his significant contributions to commutative algebra. Topics covered range from Weierstrass models and endomorphism algebras of abelian varieties to the generic Torelli theorem for hypersurfaces in compact irreducible hermitian symmetric spaces. Coarse moduli spaces for curves are also discussed, along with discriminants of curves of genus 2 and arithmetic surfaces.

Comprised of 14 chapters, this volume begins by describing a basic fibration as a Weierstrass model, with emphasis on elliptic threefolds with a section. The reader is then introduced to canonical bundles of analytic surfaces of class VII0 with curves; Lifting Problem on ideal-adically complete noetherian rings; and the canonical ring of a curve. Subsequent chapters deal with algebraic surfaces for regular systems of weights; elementary transformations of algebraic vector bundles; the irreducibility of the first differential equation of Painlevé; and F-pure normal rings of dimension two. The book concludes with an assessment of the existence of some curves.

This monograph will be a useful resource for practitioners and researchers in algebra and geometry.

On Weierstrass Models

Canonical Bundles of Analytic Surfaces of Class VII0

Ideal-Adic Completion of Noetherian Rings II

Endomorphism Algebras of Abelian Varieties

On the Canonical Ring of a Curve

Algebraic Surfaces for Regular Systems of Weights (with an Appendix by Isao Naruki)

Generic Torelli Theorem for Hypersurfaces in Compact Irreducible Hermitian Symmetric Spaces

A Variety Which Contains a P1-Fiber Space as an Ample Divisor

How Coarse the Coarse Moduli Spaces for Curves Are!

Elementary Transformations of Algebraic Vector Bundles II

Discriminants of Curves of Genus 2 and Arithmetic Surfaces

On the Irreducibility of the First Differential Equation of Painlevé

Study of F-purity in Dimension Two

A Note on the Existence of Some Curves