Positive divisors and Poincaré series on variable Riemann surfaces
type: Item
instance of: scholarly article
title: Positive divisors and Poincaré series on variable Riemann surfaces
zbMATH Open document ID: 0616.30043
author: Clifford J. Earle
author: Irwin Kra
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1987-01-01T00:00:00Z
review text: Let \(\pi:V_ p\to T_ p\) be the universal Teichmüller curve over the Teichmüller space \(T_ p\) of closed Riemann surfaces of genus \(p\geq 2\). The zero set of a suitable holomorphic section of a line bundle \(L\to V_ p\) defines a positive divisor on each closed Riemann surface \(\pi ^{-1}(t)\), \(t\in T_ p\). An explicit construction of such sections by Poincaré series produces divisors of any degree \(\geq 4p-4\), and linear algebra then produces divisors of any degree \(\geq 2p-2\), including divisors of Prym differentials. \textit{L. Bers} [Bull. Am. Math. Soc. 67, 206-210 (1961; Zbl 0102.067)] constructed canonical divisors by essentially the same methods.
Mathematics Subject Classification ID: 30F10
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14H10
zbMATH DE Number: 3998188
zbMATH Keywords: Teichmüller curve
zbMATH Keywords: positive divisor
zbMATH Keywords: Poincaré series
zbMATH Keywords: divisors of Prym differentials
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228288
OpenAlex ID: W1997441419
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DOI: 10.2748/TMJ/1178228288
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description: scientific article; zbMATH DE number 3998188