TL;DR
This paper presents an example of a divisor on a curve that cannot be realized as a trace divisor of any foliation, highlighting limitations in the correspondence between divisors and foliations.
Contribution
It provides a specific counterexample demonstrating that not all divisors are trace divisors of foliations, challenging assumptions in the theory.
Findings
Identified a divisor not realizable as a trace divisor
Showed limitations in foliation-divisor correspondence
Contributed to understanding of foliation structures
Abstract
An example is given of a divisor of a curve which is not a trace divisor of a foliation.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Algebraic Geometry and Number Theory · Geometric and Algebraic Topology