We investigate the modular properties of nodal curves on a low genus K3 surface. We prove that a general genus g curve C is the normalization of a δ-nodal curve X sitting on a primitively polarized K3 surface S of degree 2p - 2, for 2 ≤ g = p - δ < p ≤ 11. The proof is based on a local deformation-theoretic analysis of the map from the stack of pairs (S, X) to the moduli stack of curves Mg that associates to X the isomorphism class [C] of its normalization.
Flamini, F., Knutsen, A.l., Pacienza, G., Sernesi, E. (2008). Nodal Curves with General Moduli on K3 Surfaces. COMMUNICATIONS IN ALGEBRA, 36(11), 3955-3971 [10.1080/00927870802174082].
Nodal Curves with General Moduli on K3 Surfaces
SERNESI, Edoardo
2008-01-01
Abstract
We investigate the modular properties of nodal curves on a low genus K3 surface. We prove that a general genus g curve C is the normalization of a δ-nodal curve X sitting on a primitively polarized K3 surface S of degree 2p - 2, for 2 ≤ g = p - δ < p ≤ 11. The proof is based on a local deformation-theoretic analysis of the map from the stack of pairs (S, X) to the moduli stack of curves Mg that associates to X the isomorphism class [C] of its normalization.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
