Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Mobile Device Pairing
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)

     

Pfaffian presentations of elliptic normal curves

Author(s): Tom Fisher
Journal: Trans. Amer. Math. Soc. 362 (2010), 2525-2540.
MSC (2010): Primary 14H52; Secondary 14M12
Posted: December 11, 2009
MathSciNet review: 2584609
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We investigate certain alternating matrices of linear forms whose Pfaffians generate the homogeneous ideal of an elliptic normal curve, or one of its higher secant varieties.


References:

[AR]
A. Adler, S. Ramanan, Moduli of abelian varieties, Lecture Notes in Mathematics, 1644, Springer-Verlag, Berlin, 1996. MR 1621185 (2000b:14057)

[A]
M.F. Atiyah, Vector bundles over an elliptic curve, Proc. London Math. Soc. (3) 7 (1957) 414-452. MR 0131423 (24:A1274)

[ADHPR]
A. Aure, W. Decker, K. Hulek, S. Popescu, K. Ranestad, Syzygies of abelian and bielliptic surfaces in $ \mathbb{P}^4$, Internat. J. Math. 8 (1997), no. 7, 849-919. MR 1482969 (99a:14049)

[BH]
W. Bruns, J. Herzog, Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics 39, Cambridge University Press, 1993. MR 1251956 (95h:13020)

[BE1]
D.A. Buchsbaum and D. Eisenbud, Gorenstein ideals of height $ 3$, Seminar D. Eisenbud/B. Singh/W. Vogel, Vol. 2, pp. 30-48, Teubner-Texte zur Math., 48, Teubner, Leipzig, 1982. MR 686456 (84i:13017)

[BE2]
D.A. Buchsbaum and D. Eisenbud, Algebra structures for finite free resolutions, and some structure theorems for ideals of codimension 3, Amer. J. Math. 99 (1977) 447-485. MR 0453723 (56:11983)

[E]
D. Eisenbud, Commutative algebra with a view toward algebraic geometry, GTM 150, Springer-Verlag, New York, 1995. MR 1322960 (97a:13001)

[EKS]
D. Eisenbud, J. Koh, M. Stillman, Determinantal equations for curves of high degree, Amer. J. Math. 110 (1988), no. 3, 513-539. MR 944326 (89g:14023)

[F]
T.A. Fisher, On 5 and 7 descents for elliptic curves, Ph.D. thesis, University of Cambridge, 2000.

[GP]
M. Gross, S. Popescu, Equations of $ (1,d)$-polarized abelian surfaces, Math. Ann. 310 (1998), no. 2, 333-377. MR 1602020 (99d:14046)

[H]
K. Hulek, Projective geometry of elliptic curves, Soc. Math. de France, Astérisque 137 (1986). MR 845383 (88c:14046)

[Kl]
F. Klein, Über die elliptischen Normalkurven der $ n$-ten Ordnung (1885), in Gesammelte Mathematische Abhandlungen, 3: Elliptische Funktionen etc., R. Fricke et al. (eds.), Springer (1923).

[Kn]
A.J. Knight, Primals passing multiply through elliptic normal curves, Proc. London Math. Soc. (3) 23 (1971), 445-458. MR 0291173 (45:267)

[KM]
A.R. Kustin, M. Miller, Constructing big Gorenstein ideals from small ones, J. Algebra 85 (1983), no. 2, 303-322. MR 725084 (85f:13014)

[L]
H. Lange, Higher secant varieties of curves and the theorem of Nagata on ruled surfaces, Manuscripta Math. 47 (1984), no. 1-3, 263-269. MR 744323 (85f:14043)

[Ra]
M.S. Ravi, Determinantal equations for secant varieties of curves, Comm. Algebra 22 (1994), no. 8, 3103-3106. MR 1272376 (95c:14029)

[Ro]
T.G. Room, The geometry of determinantal loci, Cambridge University Press, 1938.

[vBH]
H.-Chr. Graf v. Bothmer, K. Hulek, Geometric syzygies of elliptic normal curves and their secant varieties, Manuscripta Math. 113 (2004), no. 1, 35-68. MR 2135560 (2006b:14009)

[V]
J. Vélu, Courbes elliptiques munies d'un sous-groupe $ \mathbb{Z}/n\mathbb{Z} \times \mu_n$, Bull. Soc. Math. France Mém. No. 57 (1978), 5-152. MR 507751 (80a:14011)


Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 14H52, 14M12

Retrieve articles in all Journals with MSC (2010): 14H52, 14M12


Additional Information:

Tom Fisher
Affiliation: Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, United Kingdom
Email: T.A.Fisher@dpmms.cam.ac.uk

DOI: 10.1090/S0002-9947-09-04876-4
PII: S 0002-9947(09)04876-4
Received by editor(s): June 1, 2006, and in revised form, March 17, 2008
Posted: December 11, 2009
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia