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Dimension counts for limit linear series on curves not of compact type. (English) Zbl 1378.14032

Summary: We first prove a generalized Brill-Noether theorem for linear series with prescribed multivanishing sequences on smooth curves. We then apply this theorem to prove that spaces of limit linear series have the expected dimension for curves of pseudocompact type, whenever the gluing conditions in the definition of limit linear series impose the maximal codimension. Finally, we investigate these gluing conditions in specific families of curves, showing expected dimension in several cases, each with different behavior. One of these families sheds new light on the work of F. Cools et al. [Adv. Math. 230, No. 2, 759–776 (2012; Zbl 1325.14080)] in tropical Brill-Noether theory, and suggests directions of further work in that setting.

MSC:

14H51 Special divisors on curves (gonality, Brill-Noether theory)
14H10 Families, moduli of curves (algebraic)
14C20 Divisors, linear systems, invertible sheaves
14T05 Tropical geometry (MSC2010)

Citations:

Zbl 1325.14080
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References:

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