Generalized Jouanolou duality, weakly Gorenstein rings, and applications to blowup algebras
-
Yairon Cid-Ruiz
,
Claudia Polini
Abstract
We provide a generalization of Jouanolou duality that is applicable to a plethora of situations. The environment where this generalized duality takes place is a new class of rings, that we introduce and call weakly Gorenstein rings. As a consequence, we obtain a new general framework to investigate blowup algebras. We use our results to study and determine the defining equations of the Rees algebra for certain families of ideals.
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-2201110
Award Identifier / Grant number: DMS-2201149
Funding statement: Claudia Polini was partially supported by NSF grant DMS-2201110. Bernd Ulrich was partially supported by NSF grant DMS-2201149.
Acknowledgements
We thank the reviewer for carefully reading our paper and for several comments and corrections. Yairon Cid-Ruiz is grateful to the mathematics departments of Purdue University and the University of Notre Dame, where the majority of the work was done, for their hospitality and for excellent working conditions.
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Articles in the same Issue
- Frontmatter
- No compact split limit Ricci flow of type II from the blow-down
- Deriving Perelman’s entropy from Colding’s monotonic volume
- Gravitational instantons with 𝑆1 symmetry
- Relatively Anosov groups: finiteness, measure of maximal entropy, and reparameterization
- On the Rapoport--Zink space for GU(2, 4) over a ramified prime
- Generalized Jouanolou duality, weakly Gorenstein rings, and applications to blowup algebras
- On polynomial convergence to tangent cones for singular Kähler–Einstein metrics
- Anomaly flow: Shi-type estimates and long-time existence
Articles in the same Issue
- Frontmatter
- No compact split limit Ricci flow of type II from the blow-down
- Deriving Perelman’s entropy from Colding’s monotonic volume
- Gravitational instantons with 𝑆1 symmetry
- Relatively Anosov groups: finiteness, measure of maximal entropy, and reparameterization
- On the Rapoport--Zink space for GU(2, 4) over a ramified prime
- Generalized Jouanolou duality, weakly Gorenstein rings, and applications to blowup algebras
- On polynomial convergence to tangent cones for singular Kähler–Einstein metrics
- Anomaly flow: Shi-type estimates and long-time existence
