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Paper detail

Limit linear series and ranks of multiplication maps

We develop a new technique for studying ranks of multiplication maps for linear series via limit linear series and degenerations to chains of genus-1 curves. We use this approach to prove a purely elementary criterion for proving cases of the Maximal Rank Conjecture, and then apply the criterion to several ranges of cases, giving a new proof of the case of quadrics, and also treating several families in the case of cubics. Our proofs do not require restrictions on direction of approach, so we recover new information on the locus in the moduli space of curves on which the maximal rank condition fails.

preprint2020arXivOpen access
Fu LiuBrian OssermanMontserrat Teixidor I BigasNaizhen Zhang
math.AG
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Fu LiuBrian OssermanMontserrat Teixidor I BigasNaizhen Zhang

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