Neutral linear series and Brill-Noether theory of singular curves
On a projective nonsingular curve C of genus g the variety Nr n(A) of neutral linear series parameterizes linear series of degree n and dimension r to which a given effective divisor A of degree s does not impose independent conditions. Edoardo Sernesi proved that, in the appropriate ranges of g...
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| Format: | Article |
| Language: | English |
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Sapienza Università Editrice
2017-06-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
| Online Access: | http://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2017(2)/171-174.pdf |
| Summary: | On a projective nonsingular curve C of genus g the variety Nr
n(A) of neutral linear
series parameterizes linear series of degree n and dimension r to which a given effective divisor
A of degree s does not impose independent conditions. Edoardo Sernesi proved that, in the
appropriate ranges of g, r, n, s, if C is a Brill-Noether curve then Nr
n(A) is non-empty. As an
application, here we deduce a Brill-Noether existence theorem for irreducible curves obtained
from a Brill-Noether curve by identifying a pair of points to an ordinary node.
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| ISSN: | 1120-7183 2532-3350 |