Arithmetic and Geometry: Papers Dedicated to I.R. Shafarevich on the Occasion of His Sixtieth Birthday. Volume II: Geometry

Professor V. I. Arnold (auth.), Michael Artin, John Tate (eds.)3764311118, 3764330007, 3764330023, 376433004X

Volume II Geometry.- Some Algebro-Geometrical Aspects of the Newton Attraction Theory.- Smoothing of a Ring Homomorphism Along a Section.- Convexity and Loop Groups.- The Jacobian Conjecture and Inverse Degrees.- Some Observations on the Infinitesimal Period Relations for Regular Threefolds with Trivial Canonical Bundle.- On Nash Blowing-Up.- Arrangements of Lines and Algebraic Surfaces.- Regular Functions on Certain Infinitedimensional Groups.- Examples of Surfaces of General Type with Vector Fields.- Flag Superspaces and Supersymmetric Yang-Mills Equations.- Algebraic Surfaces and the Arithmetic of Braids, I.- Towards an Enumerative Geometry of the Moduli Space of Curves.- Schubert Varieties and the Variety of Complexes.- A Crystalline Torelli Theorem for Supersingular K3 Surfaces.- Decomposition of Toric Morphisms.- A Solution to Hironaka’s Polyhedra Game.- On the Superpositions of Mathematical Instantons.- How Many Kahler Metrics Has a K3 Surface?.- On the Problem of Irreducibility of the Algebraic System of Irreducible Plane Curves of a Given Order and Having a Given Number of Nodes.

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Table of contents :
Front Matter….Pages i-vii
Some Algebro-Geometrical Aspects of the Newton Attraction Theory….Pages 1-3
Smoothing of a Ring Homomorphism Along a Section….Pages 5-31
Convexity and Loop Groups….Pages 33-63
The Jacobian Conjecture and Inverse Degrees….Pages 65-75
Some Observations on the Infinitesimal Period Relations for Regular Threefolds with Trivial Canonical Bundle….Pages 77-102
On Nash Blowing-Up….Pages 103-111
Arrangements of Lines and Algebraic Surfaces….Pages 113-140
Regular Functions on Certain Infinite-dimensional Groups….Pages 141-166
Examples of Surfaces of General Type with Vector Fields….Pages 167-173
Flag Superspaces and Supersymmetric Yang-Mills Equations….Pages 175-198
Algebraic Surfaces and the Arithmetic of Braids, I….Pages 199-269
Towards an Enumerative Geometry of the Moduli Space of Curves….Pages 271-328
Schubert Varieties and the Variety of Complexes….Pages 329-359
A Crystalline Torelli Theorem for Supersingular K3 Surfaces….Pages 361-394
Decomposition of Toric Morphisms….Pages 395-418
A Solution to Hironaka’s Polyhedra Game….Pages 419-432
On the Superpositions of Mathematical Instantons….Pages 433-450
How Many Kähler Metrics Has a K-3 Surface?….Pages 451-463
On the Problem of Irreducibility of the Algebraic System of Irreducible Plane Curves of a Given Order and Having a Given Number of Nodes….Pages 465-481
Back Matter….Pages 483-487