Moduli Spaces of Polynomials in Two Variables.

Intro -- Contents -- Introduction -- Chapter 1. Automorphisms of the affine plane -- 1.1. Blowing ups and graphs -- 1.2. Automorphisms of the affine plane -- Chapter 2. A partition on C[x,y] -- 2.1. Parental systems and graphs -- 2.2. The partition -- 2.3. Automorphisms and orderings of graphs -- Chapter 3. The geometry of the partition -- 3.1. Basic definitions -- 3.2. Varieties parametrizing infinitely near points -- 3.3. The algebraicity of the subsets of the partition -- 3.4. The geometry of the subsets of the partition -- Chapter 4. The action of Aut(C[sup(2)]) on C[x,y] -- 4.1. The action of Aut(C[sup(2)]) at the combinatorial level -- 4.2. Degree and composition by automorphisms -- 4.3. Invariance of the behaviour graph by translations on the left -- Chapter 5. The moduli problem -- 5.1. The moduli problem: groupoid approach -- 5.2. Comparison of groupoids -- Chapter 6. The moduli spaces -- 6.1. Combinatorial preliminaries -- 6.2. Construction of the moduli spaces -- 6.3. On the geometry of the moduli spaces -- Appendix A. Canonical orders -- Bibliography.

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