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Curves in Grassmannians
Author(s):
Montserrat
Teixidor i Bigas
Journal:
Proc. Amer. Math. Soc.
126
(1998),
1597-1603.
MSC (1991):
Primary 14F05, 14H10;
Secondary 14H45
MathSciNet review:
1459153
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Abstract:
This paper considers curves in Grassmannians which are themselves immersed in projective space by the Plücker map. It is shown that for a generic vector bundle of high enough degree, the image curve lies in a proper linear subvariety of this projective space and satisfies good conditions on syzygies as a curve in this subspace. For very small degree and generic vector bundle, the curve is non-degenerate.
References:
- [B]
- D.Butler, Normal generation of vector bundles over a curve, J.Diff.Geom. 39 (1994), 1-34. MR 94k:14024
- [C]
- G.Castelnuovo, Sui multipli di una serie di gruppi di punti appartenente ad una curva algebrica, Rend.Circ.Mat.Palermo 7 (1892), 99-119.
- [G]
- M.Green, Koszul cohomology and the geometry of projective varieties, J.Diff.Geom. 19 (1984), 125-171. MR 85e:14022
- [M]
- D.Mumbord, Varieties defined by quadratic equations, Corso CIME : Questions on algebraic varieties, Rome, 1970, pp. 324-327. MR 44:209
- [SD]
- B.Saint-Donat, Sur les equations definissant une courbe algebrique, C.R.Acad.Sc.Paris 274 (1972), 324-327. MR 44:6705a
- [W]
- G.Welters, Polarised abelian varieties and the heat equation., Comp.Math. 49 (1983), 173-194. MR 85f:14045
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Additional Information:
Montserrat
Teixidor i Bigas
Affiliation:
Department of Mathematics, Tufts University, Medford, Massachusetts 02155
Address at time of publication:
D.P.M.M.S., 16 Mills Lane, Cambridge CB2 1SB, England
Email:
mteixido@tufts.edu, teixidor@dpmms.cam.ac.uk
DOI:
10.1090/S0002-9939-98-04475-X
PII:
S 0002-9939(98)04475-X
Keywords:
Algebraic curve,
Grassmannian,
vector bundle,
projective normality,
syzygy
Received by editor(s):
November 8, 1996
Communicated by:
Ron Donagi
Copyright of article:
Copyright
1998,
American Mathematical Society
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