Geodesic
Degeneration of a~graph describing conformal structure
Sbornik. Mathematics, Tome 214 (2023) no. 3, pp. 383-395

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the cell decomposition of the moduli space of real genus $2$ curves with marked point on the unique real oval. The cells are enumerated by certain graphs, whose weights describe the complex structure on the curve. We show that the collapse of an edge in a graph results in a root-like singularity of the natural map from the weights on graphs to the moduli space of curves. Bibliography: 24 titles.
Keywords: real algebraic curve, abelian integral, graphs, foliation associated with a quadratic differential.
Mots-clés : moduli space 
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     author = {A. B. Bogatyrev},
     title = {Degeneration of a~graph describing conformal structure},
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     url = {http://geodesic.mathdoc.fr/item/SM_2023_214_3_a4/}
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A. B. Bogatyrev. Degeneration of a~graph describing conformal structure. Sbornik. Mathematics, Tome 214 (2023) no. 3, pp. 383-395. http://geodesic.mathdoc.fr/item/SM_2023_214_3_a4/