Hyperelliptic components of the moduli spaces of quadratic differentials with prescribed singularities

By Erwan Lanneau. 2002

93 citations recorded by the source corpus.

Abstract Moduli spaces of quadratic differentials with prescribed singularities are not necessarily connected. We describe here all cases when they have a special hyperelliptic connected component. We announce the general classification theorem: up to the four exceptional cases in low dimensional stratum, any stratum of meromorphic quadratic differentials is either connected, or has exactly two connected components. In this last case, one component is hyperelliptic, the other not.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/027e498b1322a3174098e80c6db25e6d2fbfa220

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In Geometry and Topology

1. Simion Filip
2. A. Zorich
3. Martin Moeller
4. Carlos Matheus
5. G. Forni
6. Dawei Chen
7. Martin Möller
8. M. Kontsevich

In Mathematical Physics

1. Martin Moeller
2. A. Zorich
3. Simion Filip
4. Carlos Matheus
5. Dawei Chen
6. G. Forni
7. M. Kontsevich
8. Curtis T. McMullen

In Statistical and Nonlinear Physics

1. A. Zorich
2. Carlos Matheus
3. Simion Filip
4. Martin Moeller
5. Dawei Chen
6. M. Kontsevich
7. G. Forni
8. Curtis T. McMullen

Citations in the corpus

• Teichmüller curves in genus two: Discriminant and spin (2005, background): “structures to determine the components of the strata Mg(p1, . . . , pk) of holomorphic 1-forms with zeros of prescribed multiplicity [ KZ ].”
• Quadratic differentials in low genus: exceptional and non-varying (2012, background): “This was shown by [15] and can also be quickly retrieved in our language.”
• On the minimum dilatation of pseudo-Anosov homeomorphisms on surfaces of small genus (2009, background): “It can be shown that τ is affine for the metric determined by φ (see [16]).”
• SQUARE-TILED CYCLIC COVERS (2010, background): “The remaining two strata, namely Q(2,1,1) and Q(1,1,1,1), have effective genera two and three respectively; both of them are hyperelliptic, see [24].”
• Connected components of the moduli spaces of Abelian differentials with prescribed singularities (2002, methodology): “In the present paper we give a classification of extended Rauzy classes using not only combinatorics but also tools of algebraic geometry, topology and of dynamical systems.”
• Splitting mixed Hodge structures over affine invariant manifolds (2013, methodology): “This construction is described analytically, e.g., in [Lan04, Construction 1] and algebraically as follows.”