On the locus of Prym curves where the Prym-canonical map is not an embedding

Ciliberto, Ciro; Dedieu, Thomas; Galati, Concettina; Knutsen, Andreas Leopold

doi:10.4310/arkiv.2020.v58.n1.a5

Cited by 6 publications

(19 citation statements)

References 8 publications

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“…Lemma 3.1. The differential of c g,φ at (S, H, C) (resp., of c 2g−1 at ( S, H, C)) is the morphism (8). Its kernel is H 1 (T S (−C)) (resp., H 1 (T S (− C))).…”

Section: Generalities On Moduli Mapsmentioning

confidence: 99%

“…• R 0 g -the locally closed locus in R g of pairs (C, η) for which the complete linear system |ω C (η)| is base point free and the map C → P g−2 it defines (the socalled Prym-canonical map) is not an embedding. This locus is irreducible (and unirational) of dimension 2g +1 for g 5 by [8,Thm. 1].…”

Section: Introductionmentioning

confidence: 99%

“…• D 0 5 -the locally closed locus in R 0 5 of pairs (C, η) with 4-nodal Prym-canonical model. By [8,Prop. 5.3] this locus is an irreducible (unirational) divisor in R 0 5 whose closure in R 5 coincides with closure of the locus of pairs (C, η) carrying a theta-characteristic θ such that h 0 (θ) = h 0 (θ + η) = 2.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, for the general element, the Prym-canonical map is birational onto its image, which has precisely two nodes, cf. [8,Prop. 1.2].…”

Section: Introductionmentioning

confidence: 99%

“…• R 0,nb g -the closed locus in R 0 g of pairs (C, η) for which the Prym-canonical map is not birational onto its image. This locus is irreducible of dimension 2g − 2 for g 4 and dominates the bielliptic locus in M g via the forgetful map R g → M g by [8,Cor. 2.2].…”

Section: Introductionmentioning

confidence: 99%

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Moduli of curves on Enriques surfaces

Ciliberto¹,

Dedieu²,

Galati³

et al. 2020

Advances in Mathematics

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“…Lemma 3.1. The differential of c g,φ at (S, H, C) (resp., of c 2g−1 at ( S, H, C)) is the morphism (8). Its kernel is H 1 (T S (−C)) (resp., H 1 (T S (− C))).…”

Section: Generalities On Moduli Mapsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Moreover, for the general element, the Prym-canonical map is birational onto its image, which has precisely two nodes, cf. [8,Prop. 1.2].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Moduli of curves on Enriques surfaces

Ciliberto¹,

Dedieu²,

Galati³

et al. 2020

Advances in Mathematics

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Ulrich bundles on a general blow-up of the plane

Ciliberto

Flamini

Knutsen

2023

Annali di Matematica

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We prove that on $$X_n$$ X n , the plane blown-up at n very general points, there are Ulrich line bundles with respect to a line bundle corresponding to curves of degree m passing simply through the n blown-up points, with $$m\leqslant 2\sqrt{n}$$ m ⩽ 2 n and such that the line bundle in question is very ample on $$X_n$$ X n . We prove that the number of these Ulrich line bundles tends to infinity with n. We also prove the existence of slope-stable rank-r Ulrich vector bundles on $$X_n$$ X n , for $$n\geqslant 2$$ n ⩾ 2 and any $$r \geqslant 1$$ r ⩾ 1 and we compute the dimensions of their moduli spaces. These computations imply that $$X_n$$ X n is Ulrich wild.

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