Real normalized differentials and Arbarello’s conjecture
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Using meromorphic differentials with real periods, we prove Arbarello’s conjecture that any compact complex cycle of dimension g - n in the moduli space M g of smooth algebraic curves of genus g must intersect the locus of curves having a Weierstrass point of order at most n.
Key wordsmoduli space of algebraic curves integrable system real normalized differential
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- S. Diaz, “Exceptional Weierstrass points and the divisor on moduli space that they define,” Mem. Amer. Math. Soc., 56:327 (1985).Google Scholar
- J. Harris and I. Morrison, Moduli of Curves, Graduate Texts in Math., vol. 187, Springer-Verlag, New York, 1998.Google Scholar
- S. Grushevsky and I. Krichever, “The universalWhitham hierarchy and geometry of the moduli space of pointed Riemann surfaces,” in: Surveys in Differ. Geom., vol. 14, Int. Press, Somerville, MA, 2010, 111–129.Google Scholar
- S. Grushevsky and I. Krichever, Foliations on the Moduli Space of Curves, Vanishing in Cohomology, and Calogero-Moser Curves, http://arxiv.org/abs/1108.4211.
- I. Krichever and D. H. Phong, “Symplectic forms in the theory of solitons,” in: Surveys in Differ. Geom., vol. 4, Int. Press, Boston, MA, 1998, 239–313.Google Scholar