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On catalecticant perfect ideals of codimension 2. (English) Zbl 1315.13015

The authors deal with catalectican codim 2 perfect ideals. In order to be more precise, let \( R:=K[x_1,\dots,x_n]\) be a polynomial ring over a field \(K\), and \(I\) a codimension 2 perfect ideal. The authors assume that the presentation matrix of \(I\) is a generic catalecticant or a degeneration in a sense explained in the article. Depending on the cases the ring \(R/I\) may fail to be a normal domain. As it turns out, one case leads to a Cremona transformation that not seems to be observed before in the systematization. Roughly speaking, the methods consist in studying the symbolic Rees algebra associated to \(I\): \[ {\mathcal R}^{(I)}:= \bigoplus _{r\geq 0} {I}^{(r)} t^r\subset R[t]. \]

MSC:

13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
13C14 Cohen-Macaulay modules
13C40 Linkage, complete intersections and determinantal ideals
13D02 Syzygies, resolutions, complexes and commutative rings
13E15 Commutative rings and modules of finite generation or presentation; number of generators
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
14E05 Rational and birational maps
14E07 Birational automorphisms, Cremona group and generalizations
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References:

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