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On the genus of curves in a Jacobian variety

By Valeria Ornella Marcucci


We prove that the geometric genus p of a curve in a very generic Jacobian of dimension g>3 satisfies either p=g or p>2g-3. This gives a positive answer to a conjecture of Naranjo and Pirola. For low values of g the second inequality can be further improved to p>2g-2.Comment: 16 page

Topics: Mathematics - Algebraic Geometry, 14H40
Year: 2011
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