Quadratic differentials with prescribed singularities
| Autor: | Gendron, Quentin, Tahar, Guillaume |
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| Jazyk: | francouzština |
| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4153/S0008414X24000506 |
| Popis: | The local invariants of a meromorphic quadratic differential on a compact Riemann surface are the orders of zeros and poles, and the residues at the poles of even orders. The main result of this paper is that with few exceptions, every pattern of local invariants can be obtained by a quadratic differential on some Riemann surface. The exceptions are completely classified and only occur in genera zero and one. Moreover, in the case of a nonconnected stratum, we show that, with three exceptions in genus one, every invariants can be realized in each connected component of the stratum. These results are obtained using the flat metric induced by the differentials. We give an application by bounding the number of disjoint cylinders on a primitive quadratic differential. Comment: Minor improvements, accepted for publication in "Canadian Journal of Mathematics", in French language |
| Databáze: | arXiv |
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