Geometriae Dedicata

, Volume 158, Issue 1, pp 61–68 | Cite as

An affine open covering of \({\mathcal{M}_g}\) for g ≤ 5

Original Paper


We prove that the moduli space \({\mathcal{M}_g}\) of smooth curves of genus g is the union of g−1 affine open subsets for every g with 2 ≤ g ≤ 5, as predicted by an intriguing conjecture of Eduard Looijenga.


Moduli space Affine covering Ample divisor Modular form Hyperelliptic locus 

Mathematics Subject Classification (2000)

14H10 14K25 


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© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversitá degli Studi di TrentoTrentoItaly
  2. 2.Dipartimento di Matematica “Guido Castelnuovo”Universitá di Roma “La Sapienza”RomaItaly

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