On varieties of almost minimal degree in small codimension

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dc.creatorBrodmann, Markus
dc.creatorSchenzel, Peter
dc.date2005-06-14
dc.date2006-05-18
dc.date.accessioned2026-07-07T06:42:26Z
dc.date.available2026-07-07T06:42:26Z
dc.descriptionThe aim of the present exposition is to investigate varieties of almost minimal degree and of low codimension, in particular their Betti diagrams. Here minimal degree is defined as $°X = \codim X + 2.$ We describe the structure of the minimal free resolution of a variety $X$ of almost minimal degree of $\codim X \leq 4$ by listing the possible Betti diagrams. The most surprising fact is, that the non-arithmetically Cohen-Macaulay case of varieties of almost minimal degree can occur only in small dimensions (cf. Section 2 for the precise statements). Our main technical tool is a result shown by the authors (cf. \cite{BS}), which says that besides of an exceptional case, (that is the generic projection of the Veronese surface in $\mathbb P^5_K$) any non-arithmetically normal (and in particular non-arithmetically Cohen-Macaulay) variety of almost minimal degree $X \subset \mathbb P^r_K$ (which is not a cone) is contained in a variety of minimal degree $Y \subset \mathbb P^r_K$ such that $\codim(X,Y) = 1.
dc.description12 pages. J. Algebra, to appear
dc.identifierhttps://arxiv.org/abs/math/0506279
dc.identifierhttp://arxiv.org/abs/math/0506279
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/102039
dc.subjectCommutative Algebra
dc.subjectAlgebraic Geometry
dc.subject14H45; 13D02
dc.titleOn varieties of almost minimal degree in small codimension
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