caa a22 4500 475738160 CHVBK 20180406123452.0 cr unu---uuuuu 170329e20000201xx s 000 0 eng 10.1007/s002229900031 doi (NATIONALLICENCE)springer-10.1007/s002229900031 Merkl Franz Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA (e-mail: merkl@cims.nyu.edu), USA aut A Riemann Roch Theorem for infinite genus Riemann surfaces [Elektronische Daten] [Franz Merkl] Abstract. : In this article we prove a Riemann Roch Theorem for a class of holomorphic line bundles over Riemann surfaces of infinite genus. The theorem shows that the space of holomorphic sections satisfying a pointwise asymptotic growth condition has finite dimension and it provides a formula for this dimension. The gluing functions describing the surface and the transition functions defining the line bundle have to satisfy some asymptotic bounds. The theorem applies to holomorphic line bundles associated to divisors of infinite degree that assign one point to every handle on the surface. Applications of this Riemann Roch Theorem to the description of the Kadomcev Petviashvilli flow were provided in the author's doctoral thesis. Springer-Verlag Berlin Heidelberg, 2000 Inventiones mathematicae Springer Berlin Heidelberg 139/2(2000-02-01), 391-437 0020-9910 139:2<391 2000 139 222 https://doi.org/10.1007/s002229900031 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s002229900031 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Merkl Franz Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA (e-mail: merkl@cims.nyu.edu), USA aut NATIONALLICENCE 773 0- Inventiones mathematicae Springer Berlin Heidelberg 139/2(2000-02-01), 391-437 0020-9910 139:2<391 2000 139 222 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer