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The Quarterly Journal of Mathematics Advance Access originally published online on August 28, 2007
The Quarterly Journal of Mathematics 2008 59(2):163-187; doi:10.1093/qmath/ham032
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© 2007. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

SPECIAL RAMIFICATION LOCI ON THE DOUBLE PRODUCT OF A GENERAL CURVE

C. Cumino {dagger}

Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

E. Esteves {ddagger}

Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro RJ, Brazil

L. Gatto§

Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

§ Corresponding author. E-mail: letterio.gatto{at}polito.it

Received 2 March 2007;
  Abstract

Let C be a general connected, smooth, projective curve of positive genus g. For each integer i≥0, we give formulae for the number of pairs (P, Q) isin C x C off the diagonal such that (g + i – 1)Q - (i + 1)P is linearly equivalent to an effective divisor, and the number of pairs (P, Q) isin C x C off the diagonal such that (g + i + 1)Q – (i + 1)P is linearly equivalent to a moving effective divisor.

{dagger} E-mail: caterina.cumino{at}polito.it

{ddagger} E-mail: esteves{at}impa.br


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