A limit linear series moduli scheme
Annales de l'Institut Fourier, Volume 56 (2006) no. 4, p. 1165-1205

We develop a new, more functorial construction for the basic theory of limit linear series, which provides a compactification of the Eisenbud-Harris theory. In an appendix, in order to obtain the necessary dimensional lower bounds on our limit linear series scheme we develop a theory of “linked Grassmannians”; these are schemes parametrizing sub-bundles of a sequence of vector bundles, which map into one another under fixed maps of the ambient bundles.

Nous produisons une construction fonctorielle nouvelle pour la théorie fondamentale des séries linéaires limites, qui nous donne une compactification de la théorie de Eisenbud-Harris. Dans un appendice, pour obtenir les bornes inférieures dimensionnelles nécessaires pour notre schéma de séries linéaires limites nous produisons une théorie de “grassmaniennes liées”  ; ce sont des schémas paramétrisants sous-fibrés d’une suite de fibrés vectoriels, qui se transforment sous les transformations données des fibrés ambiants.

DOI : https://doi.org/10.5802/aif.2209
Classification:  14H51
Keywords: Limit linear series, compactification, linked Grassmannian
@article{AIF_2006__56_4_1165_0,
     author = {Osserman, Brian},
     title = {A limit linear series moduli scheme},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {56},
     number = {4},
     year = {2006},
     pages = {1165-1205},
     doi = {10.5802/aif.2209},
     mrnumber = {2266887},
     zbl = {1118.14037},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2006__56_4_1165_0}
}
Osserman, Brian. A limit linear series moduli scheme. Annales de l'Institut Fourier, Volume 56 (2006) no. 4, pp. 1165-1205. doi : 10.5802/aif.2209. http://www.numdam.org/item/AIF_2006__56_4_1165_0/

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