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Bibliographic Details
Main Authors: Di Gennaro, Vincenzo, Rapagnetta, Antonio, Sabatino, Pietro
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2601.17852
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Table of Contents:
  • Let $X\subset \mathbb P^r$ be a projective factorial variety of dimension $3$, degree $n$, with at worst isolated singularities. Assume that the Picard group of $X$ is generated by the hyperplane section class. Let $C\subset X$ be a projective subscheme of dimension $1$, degree $d\gg n$, and arithmetic genus $p_a(C)$. Improving a recent result by Liu, we exhibit a Castelnuovo's bound for $p_a(C)$. In the case $X$ is Calabi-Yau, our bound gives a step forward for a certain conjecture concerning the vanishing of Gopakumar-Vafa invariants of $X$.