Mathematics – Algebraic Geometry
Scientific paper
2011-02-21
Mathematics
Algebraic Geometry
16 pages
Scientific paper
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.
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