Tohoku Mathematical Journal

Double lines on quadric hypersurfaces

Edoardo Ballico and Sukmoon Huh

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We study double line structures in projective spaces and quadric hypersurfaces, and investigate the geometry of irreducible components of Hilbert scheme of curves and moduli of stable sheaves of pure dimension 1 on a smooth quadric threefold.

Article information

Tohoku Math. J. (2), Volume 70, Number 3 (2018), 447-473.

First available in Project Euclid: 21 September 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H10: Families, moduli (algebraic)
Secondary: 14D22: Fine and coarse moduli spaces 14E05: Rational and birational maps

pure sheaf locally Cohen-Macaulay curve Hilbert scheme


Ballico, Edoardo; Huh, Sukmoon. Double lines on quadric hypersurfaces. Tohoku Math. J. (2) 70 (2018), no. 3, 447--473. doi:10.2748/tmj/1537495356.

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  • E. Arbarello, M. Cornalba and P. A. Griffiths, Geometry of algebraic curves Vol. II with a contribution by J. Harris. Springer-Verlag, 2011.
  • M. F. Atiyah, Vector bundles over an elliptic curve, Proc. London Math. Soc. (3) 7 (1957), 414–452.
  • C. Bănică and O. Forster, Multiplicity structures on space curves, The Lefschetz centennial conference, Part I (Mexico City, 1984), Contemp. Math., vol. 58, Amer. Math. Soc., Providence, RI, 1986, pp. 47–64.
  • C. Bănică, Sur les Ext-globaux dans une déformation, Compositio Math. 44 (1981), no. 1-3, 17–27.
  • D. Bayer and D. Eisenbud, Ribbons and their canonical embeddings, Trans. Amer. Math. Soc. 347 (1995), no. 3, 719–756.
  • J. Choi, K. Chung and M. Maican, Moduli of sheaves supported on quartic space curves, Michigan Math. J. 65 (2016), no. 3, 637–671.
  • D. Eisenbud and M. Green, Clifford indices of ribbons}, Trans. Amer. Math. Soc. 347 (1995), no. 3, 757–765.
  • H. G. Freiermuth and G. Trautmann, On the moduli scheme of stable sheaves supported on cubic space curves, Amer. J. Math. 126 (2004), no. 2, 363–393.
  • R. Hartshorne, Algebraic geometry}, Springer-Verlag, New York-Heidelberg, 1977, Graduate Texts in Mathematics, No. 52.
  • R. Hartshorne, The genus of space curves}, Ann. Univ. Ferrara Sez. VII (N.S.) 40 (1994), 207–223 (1996).
  • R. Hartshorne and E. Schlesinger, Curves in the double plane. Special issue in honor of Robin Hartshorne, Comm. Algebra 28 (2000), no. 12, 5655–5676.
  • M. He, Espaces de modules de systèmes cohérents, Internat. J. Math. 9 (1998), no. 5, 545–598.
  • D. Huybrechts and M. Lehn, The geometry of moduli spaces of sheaves, second ed., Cambridge Mathematical Library, Cambridge University Press, Cambridge, 2010.
  • J. Le Potier, Faisceaux semi-stables de dimension 1 sur le plan projectif, Rev. Roumaine Math. Pures Appl. 38 (1993), no. 7-8, 635–678.
  • U. Nagel, R. Notari and M. L. Spreafico, The Hilbert scheme of degree two curves and certain ropes, Internat. J. Math. 17 (2006), no. 7, 835–867.
  • R. Piene and M. Schlessinger, On the Hilbert scheme compactification of the space of twisted cubics, Amer. J. Math. 107 (1985), no. 4, 761–774.
  • C. T. Simpson, Moduli of representations of the fundamental group of a smooth projective variety. I, Inst. Hautes Études Sci. Publ. Math. (1994), no. 79, 47–129.