Linked Grassmannians and crude limit linear series

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dc.creatorOsserman, Brian
dc.date2006-05-15
dc.date.accessioned2026-07-07T07:14:12Z
dc.date.available2026-07-07T07:14:12Z
dc.descriptionIn math.AG/0407496, a new construction of limit linear series is presented which functorializes and compactifies the original construction of Eisenbud and Harris, using a new space called the linked Grassmannian. The boundary of the compactification consists of crude limit series, and maps with positive-dimensional fibers to crude limit series of Eisenbud and Harris. In this paper, we carry out a careful analysis of the linked Grassmannian to obtain an upper bound on the dimension of the fibers of the map on crude limit series, thereby concluding an upper bound on the dimension of the locus of crude limit series, and obtaining a simple proof of the Brill-Noether theorem using only the limit linear series machinery. We also see that on a general reducible curve, even crude limit series may be smoothed to nearby fibers.
dc.description19 pages
dc.identifierhttps://arxiv.org/abs/math/0605372
dc.identifierhttp://arxiv.org/abs/math/0605372
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112781
dc.subjectAlgebraic Geometry
dc.subject14M15; 14H51
dc.titleLinked Grassmannians and crude limit linear series
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