Hartshorne says in this example that the twisted cubic curve cannot be a set-theoretical complete intersection of a smooth quadric and another surface (since the twisted cubic on the quadric has type $(1, 2)$). However, the Wikipedia entry on twisted cubic says that it is a set-theoretical complete intersection (see the section "Properties"). I tried to find the intersection of the two surfaces given in Wikipedia, and it seems that it is indeed the twisted cubic. What is wrong?
2026-03-26 18:56:33.1774551393
Problem with Example II.6.6.3 in Hartshorne
302 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in ALGEBRAIC-GEOMETRY
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