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Abel Maps and Limit Linear Series for Curves of Compact Type with Three Irreducible Components

Abel Maps and Limit Linear Series for Curves of Compact Type with Three Irreducible Components We explore the relationship between limit linear series and fibers of Abel maps for compact type curves with three components. For compact type curves with two components, given an exact Osserman limit linear series $${\mathfrak {g}}$$ g , Esteves and Osserman associated a closed subscheme $${\mathbb {P}}({\mathfrak {g}})$$ P ( g ) of the fiber of the corresponding Abel map. We generalize this definition to our case. Then, for $${\mathfrak {g}}$$ g the unique exact extension of an r-dimensional refined Eisenbud–Harris limit linear series, we find the irreducible components of $${\mathbb {P}}({\mathfrak {g}})$$ P ( g ) and we show that $${\mathbb {P}}({\mathfrak {g}})$$ P ( g ) is connected of pure dimension r, with the same Hilbert polynomial as the diagonal in $${\mathbb {P}}^{r}\times {\mathbb {P}}^{r}\times {\mathbb {P}}^{r}$$ P r × P r × P r . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

Abel Maps and Limit Linear Series for Curves of Compact Type with Three Irreducible Components

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References (8)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Sociedade Brasileira de Matemática
Subject
Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s00574-018-0071-2
Publisher site
See Article on Publisher Site

Abstract

We explore the relationship between limit linear series and fibers of Abel maps for compact type curves with three components. For compact type curves with two components, given an exact Osserman limit linear series $${\mathfrak {g}}$$ g , Esteves and Osserman associated a closed subscheme $${\mathbb {P}}({\mathfrak {g}})$$ P ( g ) of the fiber of the corresponding Abel map. We generalize this definition to our case. Then, for $${\mathfrak {g}}$$ g the unique exact extension of an r-dimensional refined Eisenbud–Harris limit linear series, we find the irreducible components of $${\mathbb {P}}({\mathfrak {g}})$$ P ( g ) and we show that $${\mathbb {P}}({\mathfrak {g}})$$ P ( g ) is connected of pure dimension r, with the same Hilbert polynomial as the diagonal in $${\mathbb {P}}^{r}\times {\mathbb {P}}^{r}\times {\mathbb {P}}^{r}$$ P r × P r × P r .

Journal

Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals

Published: Jan 15, 2018

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