Variations of Hodge structures of a Teichmüller curve
By Martin Moeller. 2006
128 citations recorded by the source corpus.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0f1139587e80b082209025b965de5c41485ef6e7
How researchers see this paper
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In Geometry and Topology
- A. Wright
- Martin Möller
- Simion Filip
- Dawei Chen
- Martin Moeller
- Matt Bainbridge
- A. Eskin
- Maryam Mirzakhani
In Mathematical Physics
- A. Wright
- Martin Möller
- Simion Filip
- Dawei Chen
- Martin Moeller
- Matt Bainbridge
- A. Eskin
- Maryam Mirzakhani
Citations in the corpus
- The field of definition of affine invariant submanifolds of the moduli space of abelian differentials (2012, methodology): “The direct sum decomposition of H1 in Theorem 1.5 was previously established in the case of Teichmüller curves by Martin Möller [Möl06], and is one of the main tools used in the study of closed SL(2,R)–orbits.”
- Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus (2011, background): “Proof Let L f !X= x B be the (‘maximal Higgs’, see [36]) line bundle whose fiber over the point corresponding to ŒX is C ! , the generating differential of the Teichmüller curve.”
- Splitting mixed Hodge structures over affine invariant manifolds (2013, methodology): “It was proved by M¨oller in [M¨ol06b] that they are defined over Q after embedding into a moduli space of abelian varieties.”
- The Deligne–Mumford compactification of the real multiplication locus and Teichmüller curves in genus 3 (2012, background): “Every algebraically primitive Teichmüller curve lies in RMO for some order O in its trace field by [Möl06b], and every Teichmüller curve has a cusp, so Theorem 1.”
- Teichmüller curves in genus two: The decagon and beyond (2005, unknown): “Of these, the Veech examples coming from regular polygons also arise in Mestre’s construction of families of curves with real multiplication [Me], and Möller shows the Jacobian of X always has special endomorphisms when ðX ;oÞ generates a Teichmüller curve [Mo].”
- Quadratic differentials in low genus: exceptional and non-varying (2012, background): “and the fact that deg F = χ (see [20]), one calculates that”
- Periodic points on Veech surfaces and the Mordell-Weil group over a Teichmüller curve (2004, methodology): “The last property is stated explicitely in [ Mo06 , Lemma 3.1] for the set of local systems {L σ ,σ ∈ Gal(L/Q)/Gal(K/Q)}.”