Good components of curves in projective spaces outside the Brill–Noether range

Ballico, Edoardo

doi:10.3906/mat-1911-106

Cited by 2 publications

(1 citation statement)

References 9 publications

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“…These are summarized in Section 2. Recently, Ballico [Bal21] has proved the existence of regular components with the expected number of moduli in the range…”

Section: Introductionmentioning

confidence: 99%

Linear series with $ρ< 0$ via thrifty lego-building

Pflueger¹

2022

Preprint

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The moduli space G r g,d → Mg parameterizing algebraic curves with a linear series of degree d and rank r has expected relative dimension ρ = g−(r+1)(g−d+r). Classical Brill-Noether theory concerns the case ρ ≥ 0; we consider the non-surjective case ρ < 0. We prove the existence of components of this moduli space with the expected relative dimension when 0 > ρ ≥ −g + 3, or 0 > ρ ≥ −Crg + O(g 5/6 ), where Cr is a constant depending on the rank of the linear series such that Cr → 3 as r → ∞. These results are proved via a two-marked-point generalization suitable for inductive arguments, and the regeneration theorem for limit linear series.

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“…These are summarized in Section 2. Recently, Ballico [Bal21] has proved the existence of regular components with the expected number of moduli in the range…”

Section: Introductionmentioning

confidence: 99%

Linear series with $ρ< 0$ via thrifty lego-building

Pflueger¹

2022

Preprint

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Linear series with ρ < 0 \rho<0 via thrifty Lego building

Pflueger

2023

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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The moduli space G g , d r → M g \mathcal{G}^{r}_{g,\smash{d}}\to\mathcal{M}_{g} parameterizing algebraic curves with a linear series of degree 𝑑 and rank 𝑟 has expected relative dimension ρ = g − ( r + 1 ) ⁢ ( g − d + r ) \rho=g-(r+1)(g-d+r) . Classical Brill–Noether theory concerns the case ρ ≥ 0 \rho\geq 0 ; we consider the non-surjective case ρ < 0 \rho<0 . We prove the existence of components of this moduli space with the expected relative dimension when 0 > ρ ≥ − g + 3 0>\rho\geq-g+3 , or 0 > ρ ≥ − C r ⁢ g + O ⁢ ( g 5 / 6 ) 0>\rho\geq-C_{r}g+\mathcal{O}(g^{5/6}) , where C r C_{r} is a constant depending on the rank of the linear series such that C r → 3 C_{r}\to 3 as r → ∞ r\to\infty . These results are proved via a two-marked-point generalization suitable for inductive arguments, and the regeneration theorem for limit linear series.

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Good components of curves in projective spaces outside the Brill–Noether range

Cited by 2 publications

References 9 publications

Linear series with $ρ< 0$ via thrifty lego-building

Linear series with $ρ< 0$ via thrifty lego-building

Linear series with ρ < 0 \rho<0 via thrifty Lego building

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