Moduli spaces of surfaces and real structures

By F. Catanese. 2001

82 citations recorded by the source corpus.

We give infinite series of groups Γ and of compact complex surfaces of general type S with fundamental group Γ such that

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/67ec2bbe6843c6a81d0953f8139dcf8be9e78315

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In Geometry and Topology

Citations in the corpus

Topological methods in moduli theory (2014, background): “The following (see [96,98]) is the main result concerning surfaces isogenous to a product, and is a stronger result than weak * rigidity.”
Chebycheff and Belyi Polynomials, Dessins d’Enfants, Beauville Surfaces and Group Theory (2006, background): “[Man01]) appeared, there were further counterexamples given by Catanese, Kharlamov-Kulikov, Catanese-Wajnryb, Bauer-Catanese-Grunewald (cf. [ Cat03 ], [K-K02],[BCG05a], [CW04]).”
A Superficial Working Guide to Deformations and Moduli (2011, background): “The question was finally answered in the negative, and in every possible way ([97],[84],[40],[48],[13].”
Some new surfaces with p g = q = 0. (2003, background): “We recall briefly the following results from [Cat00] (cf. also [ Cat03 ]):”
Differentiable and Deformation Type of Algebraic Surfaces, Real and Symplectic Structures (2007, background): “ deformation equivalent surfaces which are canonically symplectomorphic (see [Cat02] and [Cat06] for more details). We already described in Lecture 4 some easy counterexamples to this conjecture (cf. [Cat03], [KK02],[BCG05]), given by pairs of complex conjugate surfaces, which are not deformation eq”
The classification of surfaces with p_g = q = 0 isogenous to a product of curves (2006, unknown): “ (like T(2,4,8)) canquickly beanalysed bythe“generatorsandrelations”programsofMAGMA to obtain results like those just used (alternatively one can use geometric branching arguments, cf. lemma (2.3) of [Cat03]). 3.2.2 A= [2,3,8]48, B∈ N3, α(B) = 48 In this case we have B= [2,3,8]48 and |G| = 2304. Eve”
Beauville surfaces without real structures (2004, background): “2. Let Gbe a ﬁnite group and u 1,u 2 ∈ M(G). Then S(u 1) is biholomorphic to S(u 2) if and only if u 1 is in the AM(G)-orbit of u 2. Proof. This Proposition follows (as Proposition 3.3) from [Cat00], [Cat03] (Proposition 3.2). Let M = (G0 1,a 1,c 1;g 1), M′ = (G0 2 ;a 2,c 2;g 2). Assume that the two”