AGATHOS

Algebraic Geometry: A Total Hypertext Online System

List of Theorems

Commutative Algebra

• Hilbert Basis Theorem
• Hilbert's Nullstellensatz
• Noether Normalization Theorem
• Going Up, Going Down, and Lying Over
• Nakayama's Lemma
• Hensel's Lemma

Analysis and Topology

• de Rham's Theorem
• Weierstrass Preparation Theorem
• Chow's Theorem

Elementary Algebraic Geometry

• Lasker's Theorem
• Dimension Theorem
• Bezout's Theorem
• Fibral Dimension Theorem
• Valuative Criteria
• Nonsingular Models of Curves
• Twenty-Seven Lines
• Riemann-Roch Theorem

Advanced Algebraic Geometry

• Serre's Finiteness Theorem
• Serre Duality Theorem
• Kodaira Vanishing Theorem
• Bertini's Theorem
• Hodge Index Theorem
• Grauert's Theorem
• Zariski's Main Theorem
• Zariski's Connectedness Theorem
• Semicontinuity Theorems
• Desingularization Theorem
• Mumford-Castelnuovo Regularity Theorem

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