Towards a tropical proof of the Gieseker–Petri Theorem

Baratham, Vyassa; Jensen, David; Mata, Cristina; Nguyen, Dat; Parekh, Shalin

doi:10.1007/s13348-012-0074-z

Collect. Math.

2012

DOI: 10.1007/s13348-012-0074-z

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Towards a tropical proof of the Gieseker–Petri Theorem

Vyassa Baratham

David Jensen

Cristina Mata

et al.

Abstract: We use tropical techniques to prove a case of the Gieseker-Petri Theorem. Specifically, we show that the general curve of arbitrary genus does not admit a Gieseker-Petri special pencil.

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2014

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Tropical independence I: Shapes of divisors and a proof of the Gieseker–Petri theorem

Jensen

Payne

2014

Algebra Number Theory

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We develop a framework to apply tropical and nonarchimedean analytic methods to multiplication maps for linear series on algebraic curves, studying degenerations of these multiplications maps when the special fiber is not of compact type. As an application, we give a new proof of the Gieseker-Petri Theorem, including an explicit tropical criterion for a curve over a valued field to be Gieseker-Petri general.

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Tropical independence I: Shapes of divisors and a proof of the Gieseker–Petri theorem

Jensen

Payne

2014

Algebra Number Theory

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Towards a tropical proof of the Gieseker–Petri Theorem

Abstract: We use tropical techniques to prove a case of the Gieseker-Petri Theorem. Specifically, we show that the general curve of arbitrary genus does not admit a Gieseker-Petri special pencil.

Cited by 1 publication

References 11 publications

Tropical independence I: Shapes of divisors and a proof of the Gieseker–Petri theorem

Tropical independence I: Shapes of divisors and a proof of the Gieseker–Petri theorem

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