Geodesic
Real Normalized Differentials and Arbarello's Conjecture
Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 2, pp. 37-51

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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 $\mathcal{M}_g$ of smooth algebraic curves of genus $g$ must intersect the locus of curves having a Weierstrass point of order at most $n$.
Keywords: moduli space of algebraic curves, integrable system, real normalized differential. 
@article{FAA_2012_46_2_a4,
     author = {I. M. Krichever},
     title = {Real {Normalized} {Differentials} and {Arbarello's} {Conjecture}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {37--51},
     publisher = {mathdoc},
     volume = {46},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2012_46_2_a4/}
}
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I. M. Krichever. Real Normalized Differentials and Arbarello's Conjecture. Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 2, pp. 37-51. http://geodesic.mathdoc.fr/item/FAA_2012_46_2_a4/