Moduli of generalized line bundles on a ribbon

• Dawei Chen ^[1] ; Jesse Leo Kass ^[2]
  1. [1] Boston College

     Boston College

     City of Boston, Estados Unidos

     
  2. [2] University of South Carolina

     University of South Carolina

     Estados Unidos

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 220, Nº 2 (February 2016), 2016, págs. 822-844
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2015.07.019
• Enlaces
  • Texto completo
• Resumen

  • A ribbon is a first-order thickening of a non-singular curve. We show that a compactification of the moduli space of generalized line bundles on a ribbon is given by the Simpson moduli space of semi-stable sheaves. We then describe the geometry of this space, determining the irreducible components, connectedness, and the smooth locus.

• Referencias bibliográficas
  • Allen B. Altman, Steven L. Kleiman, Compactifying the Picard scheme. II, Am. J. Math. 101 (1) (1979) 10–41, MR 527824 (81f:14025b).
  • Dave Bayer, David Eisenbud, Ribbons and their canonical embeddings, Trans. Am. Math. Soc. 347 (3) (1995) 719–756, MR 1273472 (95g:14032).
  • Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud, Néron Models, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) (Results in Mathematics...
  • Dawei Chen, Linear series on ribbons, Proc. Am. Math. Soc. 138 (11) (2010) 3797–3805, MR 2679602 (2011j:14071).
  • Ron Donagi, Lawrence Ein, Robert Lazarsfeld, Nilpotent cones and sheaves on K3 surfaces, in: Birational Algebraic Geometry, Baltimore, MD,...
  • Jean-Marc Drézet, Faisceaux cohérents sur les courbes multiples, Collect. Math. 57 (2) (2006) 121–171, MR 2223850 (2007b:14077).
  • Jean-Marc Drézet, Moduli spaces of coherent sheaves on multiples curves, in: Algebraic Cycles, Sheaves, Shtukas, and Moduli, in: Trends Math.,...
  • Jean-Marc Drézet, Faisceaux sans torsion et faisceaux quasi localement libres sur les courbes multiples primitives, Math. Nachr. 282 (7) (2009)...
  • Jean-Marc Drézet, Sur les conditions d’existence des faisceaux semi-stables sur les courbes multiples primitives, Proc. J. Math. 249 (2) (2011)...
  • David Eisenbud, Mark Green, Clifford indices of ribbons, Trans. Am. Math. Soc. 347 (3) (1995) 757–765, MR 1273474 (95g:14033).
  • Robin Hartshorne, Deformation Theory, Graduate Texts in Mathematics, vol. 257, Springer, New York, 2010, MR 2583634 (2011c:14023).
  • Michi-Aki Inaba, On the moduli of stable sheaves on some nonreduced projective schemes, J. Algebr. Geom. 13 (1) (2004) 1–27, MR 2008714 (2004h:14020).
  • Jesse Leo Kass, Two ways to degenerate the Jacobian are the same, Algebra Number Theory 7(2) (2013) 379–404, MR 3123643.
  • Adrian Langer, Semistable sheaves in positive characteristic, Ann. Math. (2) 159 (1) (2004) 251–276, MR 2051393 (2005c:14021).
  • Robert Lazarsfeld, Positivity for vector bundles, and multiplier ideals. II, in: Positivity in Algebraic Geometry. Ergebnisse der Mathematik...
  • Qing Liu, Dino Lorenzini, Michel Raynaud, Néron models, Lie algebras, and reduction of curves of genus one, Invent. Math. 157 (3) (2004) 455–518,...
  • Joseph Le Potier, Fibrés vectoriels sur les courbes algébriques, Publications Mathématiques de l’Université Paris 7–Denis Diderot (Mathematical...
  • Masaki Maruyama, Construction of moduli spaces of stable sheaves via Simpson’s idea, in: Moduli of Vector Bundles, Sanda, 1994, Kyoto, 1994,...
  • M. Raynaud, Spécialisation du foncteur de Picard, Publ. Math. IHÉS (38) (1970) 27–76, MR 0282993 (44 #227).
  • Carlos T. Simpson, Moduli of representations of the fundamental group of a smooth projective variety. I, Publ. Math. IHÉS (79) (1994) 47–129,...
  • Jin-Gen Yang, Coherent sheaves on a fat curve, Jpn. J. Math. (N.S.) 29 (2) (2003) 315–333, MR 2035543 (2005c:14022).