TL;DR
This paper investigates the geometric properties of Jacobian quotients of algebraic curves, proving they are not uniruled for genus ≥ 5 and classifying special cases for genus 3 and 4.
Contribution
It establishes non-uniruledness for Jacobian quotients of high-genus curves and classifies cases where quotients are uniruled for lower genus.
Findings
Jacobian quotients of genus ≥ 5 curves are never uniruled.
Classified all genus 3 and 4 curves with uniruled Jacobian quotients.
Abstract
We prove that the quotient of Jacobian of a curve whose genus is greater than or equal to 5 under the action of a finite group acting on the curve is never uniruled, and classify all curves of genus 3 and 4 whose quotients of Jacobian is uniruled.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Quantum chaos and dynamical systems · Control and Dynamics of Mobile Robots