Biliaison classes of curves in 𝐏³

Strano, Rosario

doi:10.1090/S0002-9939-03-07135-1

Biliaison classes of curves in ${\mathbf {P}}^{3}$
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Proc. Amer. Math. Soc. 132 (2004), 649-658 Request permission

Abstract:

We characterize the curves in ${\mathbf {P}}^{3}$ that are minimal in their biliaison class. Such curves are exactly the curves that do not admit an elementary descending biliaison. As a consequence we have that every curve in ${\mathbf {P}}^{3}$ can be obtained from a minimal one by means of a finite sequence of ascending elementary biliaisons.

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