Irreducibility of some families of linear series with Brill-Noether number. I
David Eisenbud, Joe Harris (1989)
Annales scientifiques de l'École Normale Supérieure
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David Eisenbud, Joe Harris (1989)
Annales scientifiques de l'École Normale Supérieure
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Edoardo Ballico (1988)
Rendiconti del Seminario Matematico della Università di Padova
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Eckart Viehweg (1977)
Compositio Mathematica
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Edoardo Ballico (2009)
Open Mathematics
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Here we study the deformation theory of some maps f: X → ℙr , r = 1, 2, where X is a nodal curve and f|T is not constant for every irreducible component T of X. For r = 1 we show that the “stratification by gonality” for any subset of [...] with fixed topological type behaves like the stratification by gonality of M g.
Fernando Cukierman, Douglas Ulmer (1993)
Compositio Mathematica
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Edoardo Ballico (2003)
Czechoslovak Mathematical Journal
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Let be the moduli space of smooth complex projective curves of genus . Here we prove that the subset of formed by all curves for which some Brill-Noether locus has dimension larger than the expected one has codimension at least two in . As an application we show that if is defined over , then there exists a low degree pencil defined over .