On the complexity of counting irreducible components and computing Betti numbers of algebraic varieties / Peter Scheiblechner. 2007
Inhalt
- Introduction
- Preliminaries
- Algebraic Geometry
- Differential Forms
- Models of Computation
- Structural Complexity
- Efficient Parallel Algorithms
- Squarefree Regular Chains
- I Upper Bounds
- Transfer Results
- Counting Connected Components
- The Zeroth de Rham Cohomology
- Modified Pseudo Remainders
- Computing Differentials
- Proof of Theorem 3.1
- Counting Irreducible Components
- Hilbert Polynomial
- II Lower Bounds
- Connectedness
- Basic Notations
- Obtaining an Acyclic Configuration Graph
- Embedding the Configuration Graph
- Equations for the Embedded Graph
- Proof of Theorem 6.1
- Appendix. The Real Reachability Problem
- Betti Numbers
- III Fixing Parameters