Abstract
We associate a Poincaré series to the dimension of global sections of multiples of r line bundles on a proper variety X. We show that this series is rational on a nonsingular characteristic 0 curve, but can be irrational on a singular curve, and can be irrational in higher dimensions. We also show that the series can be irrational in positive characteristic, even on a nonsingular curve.
Dedicated to Professor Seshadri on the occasion of his 70th birthday
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© 2003 Hindustan Book Agency
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Cutkosky, S.D. (2003). Poincaré series of line bundles on varieties. In: Lakshmibai, V., et al. A Tribute to C. S. Seshadri. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-11-8_16
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DOI: https://doi.org/10.1007/978-93-86279-11-8_16
Publisher Name: Hindustan Book Agency, Gurgaon
Print ISBN: 978-81-85931-39-5
Online ISBN: 978-93-86279-11-8
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