The moduli space of quadratic rational maps
By Laura Demarco. 2004
53 citations recorded by the source corpus.
Let be the space of quadratic rational maps , modulo the action by conjugation of the group of Mobius transformations. In this paper a compactification of is defined, as a modification of Milnor's , by choosing representatives of a conjugacy class such that the measure of maximal entropy of has conformal barycenter at the origin in and taking the closure in the space of probability measures. It is shown that is the smallest compactification of such that all iterate maps extend continuously to , where is the natural compactification of coming from geometric invariant theory.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/8a3c105b69dd23d68c2711e2af3aceea1c97d54c
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Iteration at the boundary of the space of rational maps (2004, unknown): “Proof of Theorem 2. The equivalence of properties (i), (ii), and (iii) was established by Lemma 7 in Section 2. For the implication (iv) implies (i), note rst that within the space Ratd, the map f 7! f is continuous by [ Ma2 , Thm B]. Also, if g 62 I(d) is degenerate, Theorem 1(a) implies that f 7! ”
- The Space of Morphisms on Projective Space (2009, methodology): “In the complex case, see an overview by Milnor [8], and the work of DeMarco [2], [3] about compactifications of the space Md that respect the iteration map.”