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Glicci ideals

Part of: Special varieties Theory of modules and ideals

Published online by Cambridge University Press:  28 June 2013

Juan Migliore  and
Uwe Nagel
Juan Migliore
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA email [email protected]
Uwe Nagel
Affiliation:
Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, KY 40506-0027, USA email [email protected]
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Abstract

A central problem in liaison theory is to decide whether every arithmetically Cohen–Macaulay subscheme of projective $n$-space can be linked by a finite number of arithmetically Gorenstein schemes to a complete intersection. We show that this can indeed be achieved if the given scheme is also generically Gorenstein and we allow the links to take place in an $(n+ 1)$-dimensional projective space. For example, this result applies to all reduced arithmetically Cohen–Macaulay subschemes. We also show that every union of fat points in projective 3-space can be linked in the same space to a union of simple points in finitely many steps, and hence to a complete intersection in projective 4-space.

Keywords

linkageliaisonGorenstein subschemearithmetically Cohen–Macaulay subschemereduced schemefat pointsglicci

MSC classification

Secondary: 13C40: Linkage, complete intersections and determinantal ideals 14M05: Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) 14M06: Linkage
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 9 , September 2013 , pp. 1583 - 1591
Copyright
© The Author(s) 2013 

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