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The Mumford conjecture

Geoffrey Powell (2004/2005)

Séminaire Bourbaki

The Mumford Conjecture asserts that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra on the Mumford-Morita-Miller characteristic classes; this can be reformulated in terms of the classifying space B Γ ∞ derived from the mapping class groups. The conjecture admits a topological generalization, inspired by Tillmann’s theorem that B Γ ∞ admits an infinite loop space structure after applying Quillen’s plus construction. The text presents the proof by Madsen and...

The trivial locus of an analytic map germ

H. Hauser, G. Muller (1989)

Annales de l'institut Fourier

We prove: For a local analytic family { X s } s ∈ S of analytic space germs there is a largest subspace T in S such that the family is trivial over T . Moreover the reduction of T equals the germ of those points s in S for which X s is isomorphic to the special fibre X 0 .

Topological types of symmetries of elliptic-hyperelliptic Riemann surfaces and an application to moduli spaces.

José A. Bujalance, Antonio F. Costa, Ana M. Porto (2003)

RACSAM

Sea X una superficie de Riemann de género g. Diremos que la superficie X es elíptica-hiperelíptica si admite una involución conforme h de modo que X/〈h〉 tenga género uno. La involución h se llama entonces involución elíptica-hiperelíptica. Si g > 5 entonces la involución h es única, ver [1]. Llamamos simetría a toda involución anticonforme de X. Sea Aut±(X) el grupo de automorfismos conformes y anticonformes de X y σ, τ dos simetrías de X con puntos fijos y tales que {σ, hσ} y {τ, hτ} no...

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