Ribbons and their canonical embeddings
Authors:
Dave Bayer and David Eisenbud
Journal:
Trans. Amer. Math. Soc. 347 (1995), 719756
MSC:
Primary 14H45; Secondary 13D02, 14C20
MathSciNet review:
1273472
Fulltext PDF Free Access
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.
 [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 zariski.harvard.edu, login: anonymous, Password: any, cd Macaulay, binary, get M3.tar, quit, tar xf M3.tar..
 [K]
Karen
A. Chandler, Geometry of dots and ropes,
Trans. Amer. Math. Soc. 347 (1995),
no. 3, 767–784. MR 1273473
(95f:14054), http://dx.doi.org/10.1090/S00029947199512734735
 [D]
David
A. Buchsbaum and David
Eisenbud, What makes a complex exact?, J. Algebra
25 (1973), 259–268. MR 0314819
(47 #3369)
 [D]
David
Eisenbud, Green’s conjecture: an orientation for
algebraists, Free resolutions in commutative algebra and algebraic
geometry (Sundance, UT, 1990) Res. Notes Math., vol. 2, Jones and
Bartlett, Boston, MA, 1992, pp. 51–78. MR 1165318
(93e:13020)
 [D]
David
Eisenbud and Mark
Green, Clifford indices of ribbons,
Trans. Amer. Math. Soc. 347 (1995),
no. 3, 757–765. MR 1273474
(95g:14033), http://dx.doi.org/10.1090/S00029947199512734747
 [D]
David
Eisenbud and Joe
Harris, Finite projective schemes in linearly general
position, J. Algebraic Geom. 1 (1992), no. 1,
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. 314.
 [L]
LungYing
Fong, Rational ribbons and deformation of hyperelliptic
curves, J. Algebraic Geom. 2 (1993), no. 2,
295–307. MR 1203687
(94c:14020)
 [L]
Laurent
Gruson and Christian
Peskine, Courbes de l’espace projectif:
variétés de sécantes, Enumerative geometry and
classical algebraic geometry (Nice, 1981), Progr. Math., vol. 24,
Birkhäuser, Boston, Mass., 1982, pp. 1–31 (French). MR 685761
(84m:14061)
 [R]
Robin
Hartshorne, Curves with high selfintersection on algebraic
surfaces, Inst. Hautes Études Sci. Publ. Math.
36 (1969), 111–125. MR 0266924
(42 #1826)
 [K]
K.
Hulek and A.
Van de Ven, The HorrocksMumford bundle and the Ferrand
construction, Manuscripta Math. 50 (1985),
313–335. MR
784147 (86e:14005), http://dx.doi.org/10.1007/BF01168835
 [S]
S.
Lichtenbaum and M.
Schlessinger, The cotangent complex of a
morphism, Trans. Amer. Math. Soc. 128 (1967), 41–70. MR 0209339
(35 #237), http://dx.doi.org/10.1090/S00029947196702093391
 [R]
Ragni
Piene, Numerical characters of a curve in projective
𝑛space, Real and complex singularities (Proc. Ninth Nordic
Summer School/NAVF Sympos. Math., Oslo, 1976) Sijthoff and Noordhoff,
Alphen aan den Rijn, 1977, pp. 475–495. MR 0506323
(58 #22095)
 [F]
FrankOlaf
Schreyer, Syzygies of canonical curves and special linear
series, Math. Ann. 275 (1986), no. 1,
105–137. MR
849058 (87j:14052), http://dx.doi.org/10.1007/BF01458587
 [E]
Edoardo
Sernesi, Topics on families of projective schemes,
Queen’s Papers in Pure and Applied Mathematics, vol. 73,
Queen’s University, Kingston, ON, 1986. MR 869062
(88b:14006)
 [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 zariski.harvard.edu, 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), 767784. MR 1273473 (95f:14054)
 [D]
 A. Buchsbaum and D. Eisenbud, What makes a complex exact?, J. Algebra 25 (1973), 259268. 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. 5178. MR 1165318 (93e:13020)
 [D]
 Eisenbud and M. L. Green, Clifford indices of ribbons, Trans. Amer. Math. Soc. 347 (1995), 757765. MR 1273474 (95g:14033)
 [D]
 Eisenbud and J. Harris, Finite projective schemes in linearly general position, J. Algebra Geom. 46 (1992), 1530. 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. 314.
 [L]
 Y. Fong, Rational ribbons and deformation of hyperelliptic curves, J. Algebraic Geom. 2 (1993), 295307. 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. 131. MR 685761 (84m:14061)
 [R]
 Hartshorne, Curves with high self intersection on algebraic surfaces, Publ. Math. IHES 36 (1969), 111125. MR 0266924 (42:1826)
 [K]
 Hulek and A. Van de Ven, The HorrocksMumford bundle and the Ferrand construction, Manuscripts Math. 50 (1985), 313335. MR 784147 (86e:14005)
 [S]
 Lichtenbaum and M. Schlessinger, The cotangent complex of a morphism, Trans. Amer. Math. Soc. 128 (1967), 4170. MR 0209339 (35:237)
 [R]
 Piene, Numerical characters of a curve in projective space, Real and Complex Singularities, Oslo 1976, (P. Holm, ed.), Sijthoff and Noordhoff, The Netherlands, 1977, pp. 475498. MR 0506323 (58:22095)
 [F]
 O. Schreyer, Syzygies of canonical curves and special linear series, Math. Ann. 275 (1986), 105137. 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
DOI:
http://dx.doi.org/10.1090/S00029947199512734723
PII:
S 00029947(1995)12734723
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
