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Table of Contents
Introduction
A brief history of points of infinity in geometry
Quasiprojective varieties over algebraically closed fields
Intersection multiplicity
Convex polyhedra
Toric varieties over algebraically closed fields
Number of solutions on the torus: BKK bound
Number of zeroes on the affine space I: (Weighted) Bézout theorems
Intersection multiplicity at the origin
Number of zeroes on the affine space II: the general case
Minor number of a hypersurface at the origin
Beyond this book
Miscellaneous commutative algebra
Some results related to schemes
Notation
Bibliography.
A brief history of points of infinity in geometry
Quasiprojective varieties over algebraically closed fields
Intersection multiplicity
Convex polyhedra
Toric varieties over algebraically closed fields
Number of solutions on the torus: BKK bound
Number of zeroes on the affine space I: (Weighted) Bézout theorems
Intersection multiplicity at the origin
Number of zeroes on the affine space II: the general case
Minor number of a hypersurface at the origin
Beyond this book
Miscellaneous commutative algebra
Some results related to schemes
Notation
Bibliography.