On the variety of linear series on a singular curve

Ballico, E.; Fontanari, C.

Bollettino dell'Unione Matematica Italiana, Tome 5-A (2002), p. 631-639 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

Let $Y$ be an integral projective curve with $g := p_{a} (Y) \geq 2$ . For all positive integers $d$ , $r$ let $W_{d}^{r} (Y) (^{* A *})$ be the set of all $L \in {Pic}^{d} (Y)$ with $h^{0} (Y, L) \geq r + 1$ and $L$ spanned. Here we prove that if $d \leq g - 2$ , then $dim (W_{d}^{r} (Y) (^{* A *})) \leq d - 3 r$ except in a few cases (essentially if $Y$ is a double covering).

Sia $Y$ una curva proiettiva ridotta e irriducibile con $g := p_{a} (Y) \geq 2$ . Per ogni $d$ , $r$ interi positivi sia $W_{d}^{r} (Y) (^{* A *})$ l'insieme di tutti gli $L \in {Pic}^{d} (Y)$ con $h^{0} (Y, L) \geq r + 1$ e $L$ generato dalle sezioni globali. In questo lavoro si dimostra che se $d \leq g - 2$ , allora $dim (W_{d}^{r} (Y) (^{* A *})) \leq d - 3 r$ fatte salve rare eccezioni (essenzialmente il caso in cui $Y$ sia un rivestimento doppio della retta proiettiva).

Publié le : 2002-10-01

MR 1934371 | Zbl 1177.14064

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     author = {E. Ballico and C. Fontanari},
     title = {On the variety of linear series on a singular curve},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {5-A},
     year = {2002},
     pages = {631-639},
     zbl = {1177.14064},
     mrnumber = {1934371},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2002_8_5B_3_631_0}
}

Ballico, E.; Fontanari, C. On the variety of linear series on a singular curve. Bollettino dell'Unione Matematica Italiana, Tome 5-A (2002) pp. 631-639. http://gdmltest.u-ga.fr/item/BUMI_2002_8_5B_3_631_0/

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