Name:  Uwe Nagel 

Title: Double lines and their even liaison classes

Abstract: 

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\title[]{Abstract: Double lines and their even liaison classes} 

\author{U.\ Nagel}

\address{Fachbereich Mathematik und Informatik,
Universit\"at-Gesamthochschule
Paderborn, D--33095 Paderborn, Germany}
\email{uwen@uni-paderborn.de} 

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\noindent 
This talk concerns recent  joint work with R.\ Notari and M.\ L.\
Spreafico. 
 
Despite recent progress in the theory of Gorenstein liaison, the
description of
the even liaison classes  remains as one of the main open problems. In
this
talk we  discuss such  a description for certain curves of low
degree. Based on the characterization of the homogeneous ideal and the
Hartshorne-Rao module of a double line we show, that two curves of
degree
two having the same codimension $\geq2$ are evenly linked if and only if
their Hartshorne-Rao modules are 
isomorphic. In order to achieve this result we have to construct
particular
Gorenstein ideals and to consider more generally ropes supported on a
line. These ropes are certain non-reduced curves. Actually, most of our
results for double lines generalize to ropes. 

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