Hyperplane sections of linearly normal curves

Author:
E. Ballico

Journal:
Proc. Amer. Math. Soc. **122** (1994), 395-398

MSC:
Primary 14H99; Secondary 14N05

MathSciNet review:
1213855

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Abstract | References | Similar Articles | Additional Information

Abstract: A particular case of the results proved here is that a general set of *d* points in is not the hyperplane section of a linearly normal, locally complete intersection curve in if , and the characteristic of *k* is zero.

**[AC]**Enrico Arbarello and Maurizio Cornalba,*On a conjecture of Petri*, Comment. Math. Helv.**56**(1981), no. 1, 1–38 (Italian). MR**615613**, 10.1007/BF02566195**[B]**Edoardo Ballico,*Points not as hyperplane sections of projectively normal curves*, Proc. Amer. Math. Soc.**112**(1991), no. 2, 343–346. MR**1052870**, 10.1090/S0002-9939-1991-1052870-9**[BM]**Edoardo Ballico and Juan Migliore,*Smooth curves whose hyperplane section is a given set of points*, Comm. Algebra**18**(1990), no. 9, 3015–3040. MR**1063348**, 10.1080/00927879008824058**[CO]**Luca Chiantini and Ferruccio Orecchia,*Plane sections of arithmetically normal curves in 𝑃³*, Algebraic curves and projective geometry (Trento, 1988) Lecture Notes in Math., vol. 1389, Springer, Berlin, 1989, pp. 32–42. MR**1023388**, 10.1007/BFb0085922**[EH]**David Eisenbud and Joe Harris,*The dimension of the Chow variety of curves*, Compositio Math.**83**(1992), no. 3, 291–310. MR**1175942****[Ho]**Eiji Horikawa,*On deformations of holomorphic maps. I*, J. Math. Soc. Japan**25**(1973), 372–396. MR**0322209****[W1]**Charles H. Walter,*Hyperplane sections of arithmetically Cohen-Macaulay curves*, Proc. Amer. Math. Soc.**123**(1995), no. 9, 2651–2656. MR**1260185**, 10.1090/S0002-9939-1995-1260185-2**[W2]**-,*Hyperplane sections of curves of small genus*, preprint.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1213855-5

Keywords:
Projective curve,
Hilbert scheme,
locally complete intersection,
deformation functor,
normal sheaf

Article copyright:
© Copyright 1994
American Mathematical Society