2013
DOI: 10.1112/s0010437x13007227
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Glicci ideals

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… Show more

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Cited by 9 publications
(6 citation statements)
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“…In [17, Theorem 3.1], E. Gorla obtained the very broad result that every determinantal scheme is glicci, generalising the results of [24, Theorem 1.1] and [20,Theorem 4.1]. Later, J. Migliore and U. Nagel [29] showed that every arithmetically Cohen-Macaulay subscheme of P đť‘› that is generically Gorenstein is actually glicci when viewed as a subscheme of P đť‘›+1 .…”
Section: Further Context On a Question In Liaison Theorymentioning
confidence: 97%
“…In [17, Theorem 3.1], E. Gorla obtained the very broad result that every determinantal scheme is glicci, generalising the results of [24, Theorem 1.1] and [20,Theorem 4.1]. Later, J. Migliore and U. Nagel [29] showed that every arithmetically Cohen-Macaulay subscheme of P đť‘› that is generically Gorenstein is actually glicci when viewed as a subscheme of P đť‘›+1 .…”
Section: Further Context On a Question In Liaison Theorymentioning
confidence: 97%
“…There are partial results in the direction of an affirmative answer to Question 1, including the results that standard determinantal schemes [23, Theorem 1.1], mixed ladder determinantal schemes from two-sided ladders [16, Corollary 2.2], schemes of pfaffians [8, Theorem 2.3], wide classes of arithmetically Cohen-Macaulay curves in P 4 [5,6], and arithmetically Cohen-Macaulay schemes defined by Borel-fixed monomial ideals [27,Theorem 3.5] are all glicci. For more results, see [19,4,7,21,17,29].…”
Section: Liaison Theory Basicsmentioning
confidence: 99%
“…Fat points also arise indirectly in other topics of study in algebraic geometry, such as the study of secant varieties [8]. In commutative algebra ideals of fat points give a useful class of test cases and suggest interesting questions that can be true more generally (see, for example, [43], where the authors give a conjecture for all nonreduced zero-dimensional schemes, and as evidence prove it for fat points). Fat points also arise in more applied situations, such as combinatorics and in interpolation problems [46,40].…”
Section: Motivationmentioning
confidence: 99%