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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
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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 tropical geometry, Brill-Noether theory, special divisors on algebraic curves
MSC Classifications: 14T05, 14H51 show english descriptions Tropical geometry [See also 12K10, 14M25, 14N10, 52B20]
Special divisors (gonality, Brill-Noether theory)
14T05 - Tropical geometry [See also 12K10, 14M25, 14N10, 52B20]
14H51 - Special divisors (gonality, Brill-Noether theory)
 

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