Curves on a double surface

• Autores: Scott Nollet, Enrico Schlesinger
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 54, Fasc. 3, 2003, págs. 327-340
• Idioma: inglés
• Títulos paralelos:
  • Curvas en una superficie doble
• Enlaces
  • Texto completo
• Resumen

  • Let F be a smooth projective surface contained in a smooth threefold T, and let X be the scheme corresponding to the divisor 2F on T. A locally Cohen-Macaulay curve C included in X gives rise to two effective divisors on F, namely the largest divisor P contained in C intersection F and the curve R residual to C intersection F in C. We show that under suitable hypotheses a general deformation of R and P lifts to a deformation of C on X, and give applications to the study of Hilbert schemes of locally Cohen-Macaulay space curves.