On the genus of curves in a Jacobian variety
classification
🧮 math.AG
keywords
genusjacobiananswerconjecturecurvecurvesdimensioneither
read the original abstract
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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