Geometric Proofs of Some Results of Morita

Abstract

In this note we give geometric formulations and proofs of three results of S. Morita. These results relate certain two dimensional cohomology classes of various moduli spaces of curves. We also give a geometric interpretation of a fourth result of Morita. One motivation of this work is to facilitate the application of these results in our work (in preparation) on the Arakelov geometry of moduli spaces of curves.

arXiv commentLatex2e, 15 pages. In this revised version, the statements of the main results remain the same, but one proof has been clarified and improved

References in corpus (2)

• Torelli Groups and Geometry of Moduli Spaces of Curves
• Completions of mapping class groups and the cycle $C-C^{-}$

Cited by in corpus (11)

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• Symplectic Lefschetz fibrations with arbitrary fundamental groups
• Relative Pro-$\ell$ Completions of Mapping Class Groups
• Second variation of Zhang's lambda-invariant on the moduli space of curves
• Normal functions and the height of Gross-Schoen cycles
• Surface bundles and the section conjecture
• Frobenius' theta function and Arakelov invariants in genus three
• Theta functions on the theta divisor