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• W2963696679 abstract "In this article we consider moduli properties of singular curves on K3 surfaces. Let Bg denote the stack of primitively polarized K3 surfaces (X,L) of genus g and let Tg,kn→Bg be the stack parameterizing tuples [(f:C→X,L)] with f an unramified morphism which is birational onto its image, C a smooth curve of genus p(g,k)−n and f⁎C∈|kL|. We show that the forgetful morphismη:Tg,kn→Mp(g,k)−n is generically finite on at least one component, for all but finitely many values of p(g,k)−n. We further study the Brill–Noether theory of those curves parametrized by the image of η, and find a Wahl-type obstruction for a smooth curve with an unordered marking to have a nodal model on a K3 surface in such a way that the marking is the divisor over the nodes. Dans cet article, nous regardons les propriétés de modules des courbes singulières contenues dans les surfaces K3. Considérons Bg le champ classifiant des surfaces K3 de genre g munies d'une polarisation primitive (X,L), et Tg,kn→Bg le champ classifiant des paires [(f:C→X,L)], où f est un morphisme non-ramifié et birationnel sur son image, C est une courbe lisse de genre p(g,k)−n, et f⁎C∈|kL|. Nous montrons que le morphisme d'oubliη:Tg,kn→Mp(g,k)−n est génériquement fini sur au moins une composante irréductible, en dehors d'un nombre fini de valeurs pour p(g,k)−n. Par-ailleurs, nous étudions la théorie de Brill–Noether des courbes paramétrées par l'image de η. Nous trouvons une obstruction de type Wahl à ce qu'une courbe lisse munie des points marqués non-ordonnés possède un modèle nodal sur une surface K3, de telle sorte que les points marqués forment le diviseur au-dessus des nœuds." @default.
• W2963696679 created "2019-07-30" @default.
• W2963696679 creator A5042610396 @default.
• W2963696679 date "2015-11-01" @default.
• W2963696679 modified "2023-09-29" @default.
• W2963696679 title "The moduli of singular curves on K3 surfaces" @default.
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• W2963696679 doi "https://doi.org/10.1016/j.matpur.2015.05.007" @default.
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