Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Ribbons and their canonical embeddings

Authors: Dave Bayer and David Eisenbud
Journal: Trans. Amer. Math. Soc. 347 (1995), 719-756
MSC: Primary 14H45; Secondary 13D02, 14C20
MathSciNet review: 1273472
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study double structures on the projective line and on certain other varieties, with a view to having a nice family of degenerations of curves and K3 surfaces of given genus and Clifford index. Our main interest is in the canonical embeddings of these objects, with a view toward Green's Conjecture on the free resolutions of canonical curves. We give the canonical embeddings explicitly, and exhibit an approach to determining a minimal free resolution.

References [Enhancements On Off] (What's this?)

  • [D] Bayer and M. Stillman, Macaulay: A system for computation in algebraic geometry and commutative algebra, Available from the authors or by anonymous ftp as follows. ftp, login: anonymous, Password: any, cd Macaulay, binary, get M3.tar, quit, tar xf M3.tar..
  • [K] Chandler, Geometry of dots and ropes, Trans. Amer. Math. Soc. 347 (1995), 767-784. MR 1273473 (95f:14054)
  • [D] A. Buchsbaum and D. Eisenbud, What makes a complex exact?, J. Algebra 25 (1973), 259-268. MR 0314819 (47:3369)
  • [D] Eisenbud, Green's conjecture; an orientation for algebraists, Sundance 91: Proceedings of a Conference on Free Resolutions in Commutative Algebra and Algebraic Geometry, Jones and Bartlett, 1992, pp. 51-78. MR 1165318 (93e:13020)
  • [D] Eisenbud and M. L. Green, Clifford indices of ribbons, Trans. Amer. Math. Soc. 347 (1995), 757-765. MR 1273474 (95g:14033)
  • [D] Eisenbud and J. Harris, Finite projective schemes in linearly general position, J. Algebra Geom. 46 (1992), 15-30. MR 1129837 (92i:14035)
  • 1. -, On varieties of minimal degree, Algebraic Geometry; Bowdoin 1985. Proc. Sympos. Pure Math., vol. 46, part 1, Amer. Math. Soc., Providence, RI, 1987, pp. 3-14.
  • [L] -Y. Fong, Rational ribbons and deformation of hyperelliptic curves, J. Algebraic Geom. 2 (1993), 295-307. MR 1203687 (94c:14020)
  • [L] Gruson and C. Peskine, Courbes dans l'espace projectif, varietés de sécantes, Enumerative Geometry and Projective Geometry, Progress in Math., vol. 24, (P. Le Barz and Y. Hervier, eds.), Birkhäuser, Boston, MA, 1982, pp. 1-31. MR 685761 (84m:14061)
  • [R] Hartshorne, Curves with high self intersection on algebraic surfaces, Publ. Math. IHES 36 (1969), 111-125. MR 0266924 (42:1826)
  • [K] Hulek and A. Van de Ven, The Horrocks-Mumford bundle and the Ferrand construction, Manuscripts Math. 50 (1985), 313-335. MR 784147 (86e:14005)
  • [S] Lichtenbaum and M. Schlessinger, The cotangent complex of a morphism, Trans. Amer. Math. Soc. 128 (1967), 41-70. MR 0209339 (35:237)
  • [R] Piene, Numerical characters of a curve in projective $ n$-space, Real and Complex Singularities, Oslo 1976, (P. Holm, ed.), Sijthoff and Noordhoff, The Netherlands, 1977, pp. 475-498. MR 0506323 (58:22095)
  • [F] O. Schreyer, Syzygies of canonical curves and special linear series, Math. Ann. 275 (1986), 105-137. MR 849058 (87j:14052)
  • [E] Sernesi, Topics on families of projective schemes, Queen's Papers in Pure and Appl. Math. 73, Queen's Univ., Kingston, Canada, 1986. MR 869062 (88b:14006)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 14H45, 13D02, 14C20

Retrieve articles in all journals with MSC: 14H45, 13D02, 14C20

Additional Information

Keywords: Ribbon, double structure, hyperelliptic curve, Clifford index, Green's conjecture, free resolution, canonical curve, K3 surface, K3 carpet
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society