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Symbolic Rees Algebras, Eloísa Grifo, Alexandra Seceleanu
Symbolic Rees Algebras, Eloísa Grifo, Alexandra Seceleanu
Department of Mathematics: Faculty Publications
We survey old and new approaches to the study of symbolic powers of ideals. Our focus is on the symbolic Rees algebra of an ideal, viewed both as a tool to investigate its symbolic powers and as a source of challenging problems in its own right. We provide an invitation to this area of investigation by stating several open questions.
Expected Resurgence Of Ideals Defining Gorenstein Rings, Eloísa Grifo, Craig Huneke, Vivek Mukundan
Expected Resurgence Of Ideals Defining Gorenstein Rings, Eloísa Grifo, Craig Huneke, Vivek Mukundan
Department of Mathematics: Faculty Publications
Building on previous work by the same authors, we show that certain ideals defining Gorenstein rings have expected resurgence, and thus satisfy the stable Harbourne Conjecture. In prime characteristic, we can take any radical ideal defining a Gorenstein ring in a regular ring, provided its symbolic powers are given by saturations with the maximal ideal. While this property is not suitable for reduction to characteristic p, we show that a similar result holds in equicharacteristic 0 under the additional hypothesis that the symbolic Rees algebra of I is noetherian.
Results On Containments And Resurgences, With A Focus On Ideals Of Points In The Plane, Annika Denkert
Results On Containments And Resurgences, With A Focus On Ideals Of Points In The Plane, Annika Denkert
Department of Mathematics: Dissertations, Theses, and Student Research
Let K be an algebraically closed field and I ⊆ R=K[PN] a nontrivial homogeneous ideal. We can describe ordinary powers Ir and symbolic powers I(m) of I. One question that has been of interest over the past couple of years is that of when we have containment of I(m) in Ir. Bocci and Harbourne defined the resurgence of I as rho(I)=supm,r{m/r | I(m) is not contained in Ir}. Hence in particular I(m) ⊆ Ir whenever m/r is at least …