Fibred surfaces, varieties isogenous to a product and related moduli spaces

By F. Catanese. 2000

258 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8bf3b04db66e4d0f3f0e928bac03e672bf4fb206

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Citations in the corpus

Beauville surfaces without real structures (2004, methodology): “very ﬁnite group G together with groups AU(G), AM(G) acting on them. We call U(G) the set of unmixed Beauville structures and M(G) the set of mixed Beauville structures on G. Using constructions from [Cat00] and [Cat03] we associate an unmixed Beauville surface S(v) to every v∈ U(G) and a mixed Beau”
Some new surfaces with p g = q = 0. (2003, background): “es isogenous to a product. Let Sbe a smooth connected algebraic surface over the complex numbers. First we will recall the notion of surfaces isogenous to a higher product of curves. By prop. 3.11 of [Cat00] the following two properties 1) and 2) of a surface are equivalent. 3 Deﬁnition 1.1 A surfac”
A Superficial Working Guide to Deformations and Moduli (2011, background): “ presence of a big fundamental group implies that a connected component of the moduli space is determined by some topological invariants. A typical case is the one of surfaces isogenous to a product ([Cat00]), where a surface is said to be isogenous to a (higher) product if and only if it is a quoti”
On totally geodesic submanifolds in the Jacobian locus (2013, background): “ of Gin the mapping class group Γ g[11]. So Gacts on the Teichmu¨ller space Tg and we denote by TG the set of ﬁxed points of Gon Tg, which is a nonempty by the solution of Nielsen realization problem [14, 27, 3], and is a complex submanifold of Tg. The tangent space to TG g at a point [C] is given b”
Topological methods in moduli theory (2014, methodology): “perelliptic involution in genus g= 3. 34 F. CATANESE Teichmu¨ller theory can be further applied in order to analyse the ﬁxed loci of ﬁnite subgroups Gof the mapping class group (see [Ker83], [Tro96], [Cat00]) Theorem 31. (Reﬁned Nielsen realization) Let G⊂ Mapg be a ﬁnite subgroup. Then Fix(G) ⊂ Tg ”
Chebycheff and Belyi Polynomials, Dessins d’Enfants, Beauville Surfaces and Group Theory (2006, methodology): “ others it is shown there that the topology of a surface isogenous to a product determines its deformation class up to complex conjugation. The following theorem contains a correction to thm. 4.14 of [Cat00]. Theorem 7.2. Let S= (C 1 ×C 2)/Gbe a surface isogenous to a product. Then any surface Xwith”
The absolute Galois group acts faithfully on regular dessins and on Beauville surfaces (2015, methodology): “Beauville surfaces were introduced by Catanese [7] following an example of Beauville, and their first properties were subsequently investigated by himself, Bauer and Grunewald [1, 2].”
The classification of surfaces with p_g = q = 0 isogenous to a product of curves (2006, methodology): “on surfaces isogenous to a product Throughout this section we assume that Sis a surface of general type. We recall ﬁrst the notion of surfaces isogenous to a product of curves. By Proposition 3.11 of [Cat00] the following two properties for a surface of general type are equivalent. Deﬁnition 2.1 A s”
Standard isotrivial fibrations with p_g=q=1, II (2007, background): “ and F so that S is isomorphic to the minimal desingularization of T := (C × F)/G. If T is smooth then S = T is called a quasi-bundle or a surface isogenous to an unmixed product (see [Se90], [Se96], [Ca00]). Quasi-bundles of general type with pg = q = 1 are classiﬁed in [Pol08] and [CarPol]. In the”
Differentiable and Deformation Type of Algebraic Surfaces, Real and Symplectic Structures (2007, background): “YPE OF ALGEBRAIC SURFACES 49 and normal locally ﬁnite coverings f: X→ Y, with general ﬁbre ∼= M, and such that for each component Ri of f−1(Di) the ramiﬁcation index divides mi. We have moreover (see [Cat00]) the following Proposition 4.8. Let Xbe a complex manifold, and Ga group of holomorphic auto”