The theta characteristic of a branched covering

By A. Eskin, A. Okounkov, R. Pandharipande. 2003

73 citations recorded by the source corpus.

Abstract We give a group-theoretic description of the parity of a pull-back of a theta characteristic under a branched covering. It involves lifting monodromy of the covering to the semidirect product of the symmetric and Clifford groups, known as the Sergeev group. As an application, we enumerate torus coverings with respect to their ramification and parity and, in particular, show that the corresponding all-degree generating functions are quasimodular forms.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bf2c7b69e7333f46f27cd2a221540630c9bf0367

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. Dawei Chen
2. Matt Bainbridge
3. Martin Moeller
4. Martin Möller
5. A. Zorich
6. Don Zagier
7. A. Eskin
8. A. Sauvaget

In Geometry and Topology

1. Dawei Chen
2. Martin Moeller
3. Carlos Matheus
4. G. Forni
5. Martin Möller
6. A. Zorich
7. A. Eskin
8. Don Zagier

In Mathematical Physics

1. Dawei Chen
2. Martin Möller
3. Martin Moeller
4. A. Zorich
5. Carlos Matheus
6. A. Eskin
7. G. Forni
8. Don Zagier

Citations in the corpus

• Introduction to Teichm\"uller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards (2013, background): “Pandharipande [28] to determine explicit formulas for volumes of connected components of strata.”
• Quasimodularity and large genus limits of Siegel-Veech constants (2016, methodology): “In [19] the volumes of the connected components of strata have been calculated individually.”
• Pillowcases and quasimodular forms (2005, background): “(3). This gives an asymptotic enumeration of pillowcase covers and, hence, computes the volume of the moduli spaces of quadratic differentials. 1.2.6 In spirit, Theorem 1 is parallel to the results of [1, 8, 13], see also [2, 3, 5] for earlier results in the physics literature. The main novelty is th”
• Masur–Veech volumes and intersection theory on moduli spaces of Abelian differentials (2019, methodology): “hyperelliptic components in Section 6.5. Along the way we revisit the counting problem for torus covers with sign given by the spin parity and complete the proof of Eskin, Okounkov and Pandharipande ([EOP08]) that the generating function is a quasimodular form of the expected weight. We then show th”
• Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow (2011, methodology): “d by M. Kontsevich and A. Zorich [KZ1] and by E. Lanneau [La1]); one needs to compute volumes of these components (they are computed in the papers of A. Eskin, A. Okounkov, and R. Pandharipande [EO], [EOPa]); one also has to know a description of the principal boundary of the components of the strat”
• Euler characteristics of Teichmüller curves in genus two (2006, methodology): “eodesic flow of a generic Abelian differential (X,ω) ∈ Swith respect to the canonical flat metric on Xdetermined by ω. Volumes of orbit closures and their applications to dynamics are studied in [EO01], [EOP], [EMS03], [EMZ03], [HL06], [LR06], and [Lel06]. A closed SL2R-orbit Slies over a Teichmu¨ller ”