On Rao's Theorems and the Lazarsfeld-Rao Property
| dc.creator | Hartshorne, Robin | |
| dc.date | 2003-02-07 | |
| dc.date.accessioned | 2026-07-07T04:55:06Z | |
| dc.date.available | 2026-07-07T04:55:06Z | |
| dc.description | Let $X$ be an integral projective scheme satisfying the condition $S_3$ of Serre and $H^1({\mathcal O}_X(n)) = 0$ for all $n \in {\mathbb Z}$. We generalize Rao's theorem by showing that biliaison equivalence classes of codimension two subschemes without embedded components are in one-to-one correspondence with pseudo-isomorphism classes of coherent sheaves on $X$ satisfying certain depth conditions. We give a new proof and generalization of Strano's strengthening of the Lazarsfeld--Rao property, showing that if a codimension two subscheme is not minimal in its biliaison class, then it admits a strictly descending elementary biliaison. For a three-dimensional arithmetically Gorenstein scheme $X$, we show that biliaison equivalence classes of curves are in one-to-one correspondence with triples $(M,P,α)$, up to shift, where $M$ is the Rao module, $P$ is a maximal Cohen--Macaulay module on the homogeneous coordinate ring of $X$, and $α: P^{\vee} \to M^* \to 0$ is a surjective map of the duals. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0302078 | |
| dc.identifier | http://arxiv.org/abs/math/0302078 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66467 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14M06; 13C40 | |
| dc.title | On Rao's Theorems and the Lazarsfeld-Rao Property | |
| dc.type | text |