On the irreducibility of the Hilbert scheme of space curves

Author:
Hristo Iliev

Journal:
Proc. Amer. Math. Soc. **134** (2006), 2823-2832

MSC (2000):
Primary 14H10; Secondary 14C05

Published electronically:
April 11, 2006

MathSciNet review:
2231604

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Abstract: Denote by the Hilbert scheme parametrizing smooth irreducible complex curves of degree and genus embedded in . In 1921 Severi claimed that is irreducible if . As it has turned out in recent years, the conjecture is true for and , while for it is incorrect. We prove that , and are irreducible, provided that , and , correspondingly. This augments the results obtained previously by Ein (1986), (1987) and by Keem and Kim (1992).

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Additional Information

**Hristo Iliev**

Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-747, Korea

Email:
itso@math.snu.ac.kr

DOI:
https://doi.org/10.1090/S0002-9939-06-08516-9

Received by editor(s):
December 10, 2003

Received by editor(s) in revised form:
April 22, 2005

Published electronically:
April 11, 2006

Additional Notes:
The author was supported in part by NIIED and KOSEF (R01-2002-000-00051-0).

Communicated by:
Michael Stillman

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.