Geodesic
Holomorphic Structure on the Space of Riemann Surfaces with Marked Boundary
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 235 (2001), pp. 98-109

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In this paper we construct a natural complex structure on the moduli space of Riemann surfaces with boundary consisting of a finite number of punctures and circles and with marked points on boundary circles. We also give a description of the tangent space to the moduli space in terms of holomorphic objects associated to the corresponding Riemann surface. 
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     author = {S. M. Ivashkovich and V. V. Shevchishin},
     title = {Holomorphic {Structure} on the {Space} of {Riemann} {Surfaces} with {Marked} {Boundary}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     year = {2001},
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     url = {http://geodesic.mathdoc.fr/item/TM_2001_235_a6/}
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S. M. Ivashkovich; V. V. Shevchishin. Holomorphic Structure on the Space of Riemann Surfaces with Marked Boundary. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 235 (2001), pp. 98-109. http://geodesic.mathdoc.fr/item/TM_2001_235_a6/