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

Mireille Martin-Deschamps, Ragni Piene

We show that the arithmetically Cohen--Macaulay (ACM) curves of degree 4 and genus 0 in ${\mathbf{P}}^4$ form an irreducible subset of the Hilbert scheme. Using this, we show that the…