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# Lifting Divisors on a Generic Chain of Loops

Published:2015-03-31
Printed: Jun 2015
• Dustin Cartwright,
Department of Mathematics , Yale University , PO Box 208283 , New Haven, CT 06520
• David Jensen,
Department of Mathematics , Yale University , PO Box 208283 , New Haven, CT 06520
• Sam Payne,
Department of Mathematics , Yale University , PO Box 208283 , New Haven, CT 06520
 Format: LaTeX MathJax PDF

## Abstract

Let $C$ be a curve over a complete valued field with infinite residue field whose skeleton is a chain of loops with generic edge lengths. We prove that any divisor on the chain of loops that is rational over the value group lifts to a divisor of the same rank on $C$, confirming a conjecture of Cools, Draisma, Robeva, and the third author.
 Keywords: tropical geometry, Brill-Noether theory, special divisors on algebraic curves
 MSC Classifications: 14T05 - Tropical geometry [See also 12K10, 14M25, 14N10, 52B20] 14H51 - Special divisors (gonality, Brill-Noether theory)

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