منابع مشابه
Covers and the Curve Complex
We propose a program of studying the coarse geometry of combinatorial moduli spaces of surfaces by classifying the quasi-isometric embeddings between them. We provide the first non-trivial examples of quasi-isometric embeddings between curve complexes. These are induced either via orbifold coverings or by puncturing a closed surface. As a corollary, we give new quasiisometric embeddings between...
متن کاملm at h . G T ] 2 8 Ju n 20 07 COVERS AND THE CURVE COMPLEX
We provide the first non-trivial examples of quasiisometric embeddings between curve complexes. These are induced either by puncturing a closed surface or via orbifold coverings. As a corollary, we give new quasi-isometric embeddings between mapping class groups.
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A finite-sheeted covering between surfaces induces a quasi-isometric embedding of the associated curve complexes.
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This note is an exposition of part of Dijkgraaf’s article [Dij] on counting covers of elliptic curves and their connection with modular forms. CONTENTS 1. Statement of the problem 1 2. From connected to disconnected covers 4 3. The monodromy map 9 4. A calculation in the symmetric group 12 5. A calculation in the group algebra 15 6. A formula of Frobenius 17 7. The work of Kaneko and Zagier 20 ...
متن کاملThe number of genus 2 covers of an elliptic curve
The main aim of this paper is to determine the number cN,D of genus 2 covers of an elliptic curve E of fixed degree N ≥ 1 and fixed discriminant divisor D ∈ Div(E). In the case that D is reduced, this formula is due to Dijkgraaf. The basic technique here for determining cN,D is to exploit the geometry of a certain compactification C = CE,N of the universal genus 2 curve over the Hurwitz space H...
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ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2009
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2009.13.2141