Displaying similar documents to “The fibre of the Prym map in genus four”

Curves of genus seven that do not satisfy the Gieseker-Petri theorem

Abel Castorena (2005)

Bollettino dell'Unione Matematica Italiana

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In the moduli space of curves of genus g , ℳ g , let 𝒢𝒫 g be the locus of curves that do not satisfy the Gieseker-Petri theorem. In the genus seven case we show that 𝒢𝒫 7 is a divisor in ℳ 7 .

Codimension 1 subvarieties ℳ g and real gonality of real curves

Edoardo Ballico (2003)

Czechoslovak Mathematical Journal

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Let ℳ g be the moduli space of smooth complex projective curves of genus g . Here we prove that the subset of ℳ g formed by all curves for which some Brill-Noether locus has dimension larger than the expected one has codimension at least two in ℳ g . As an application we show that if X ∈ ℳ g is defined over ℝ , then there exists a low degree pencil u X → ℙ 1 defined over ℝ .

On the variety of linear series on a singular curve

E. Ballico, C. Fontanari (2002)

Bollettino dell'Unione Matematica Italiana

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Let Y be an integral projective curve with g := p a ⁢ Y ≥ 2 . For all positive integers d , r let W d r ⁢ Y ⁢ * A * be the set of all L ∈ Pic d ⁢ Y with h 0 ⁢ Y , L ≥ r + 1 and L spanned. Here we prove that if d ≤ g - 2 , then dim ⁡ W d r ⁢ Y ⁢ * A * ≤ d - 3 ⁢ r except in a few cases (essentially if Y is a double covering).