Arithmetically Cohen--Macaulay curves in P^4 of degree 4 and genus 0

Details Arithmetically Cohen--Macaulay curves in P^4 of degree 4 and genus 0 Arithmetically Cohen--Macaulay curves in P^4 of degree 4 and genus 0

1996-10-15

arxiv.org/abs/alg-geom/9610016v1

Mathematics

Algebraic Geometry

17 pages, AMSTeX

Scientific paper

We show that the arithmetically Cohen--Macaulay (ACM) curves of degree 4 and
genus 0 in ${\bold P}^4$ form an irreducible subset of the Hilbert scheme.
Using this, we show that the singular locus of the corresponding component of
the Hilbert scheme has dimension greater than 6. Moreover, we describe the
structures of all ACM curves of Hilb$^{4m+1}({\bold P}^4)$.

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