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- Title
Glicci ideals.
- Authors
Migliore, Juan; Nagel, Uwe
- 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.
- Subjects
LIAISON theory (Mathematics); ARITHMETIC; MODULES (Algebra); COHEN-Macaulay modules; PROJECTIVE spaces; APPLIED mathematics; MATHEMATICAL analysis
- Publication
Compositio Mathematica, 2013, Vol 149, Issue 9, p1583
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X13007227