A remark on a conjecture of Hain and Looijenga

Mathematics – Algebraic Geometry

Scientific paper

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5 pages

Scientific paper

After recalling the various tautological algebras of the moduli space of
curves and some of its partial compactifications and stating several well-known
results and conjectures concerning these algebras, we prove that the natural
extension to the case of pointed curves of a 1996 conjecture of Hain and
Looijenga is true if and only if two of the stated conjectures are true.

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