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Abstract A major open question in the theory of Gorenstein liaison is whether or not every arithmetically Cohen–Macaulay subscheme of can be G‐linked to a complete intersection. Migliore and Nagel showed that if such a scheme is generically Gorenstein (e.g., reduced), then, after re‐embedding so that it is viewed as a subscheme of , indeed it can be G‐linked to a complete intersection. Motivated by this result, we consider techniques for constructing G‐links on a scheme from G‐links on a closely related reduced scheme. Polarization is a tool for producing a squarefree monomial ideal from an arbitrary monomial ideal. Basic double G‐links on squarefree monomial ideals can be induced from vertex decompositions of their Stanley–Reisner complexes. Given a monomial ideal and a vertex decomposition of the Stanley–Reisner complex of its polarization , we give conditions that allow for the lifting of an associated basic double G‐link of to a basic double G‐link of itself. We use the relationship we develop in the process to show that the Stanley–Reisner complexes of polarizations of stable Cohen– Macaulay monomial ideals are vertex decomposable. We then introduce and study polarization of a Gröbner basis of an arbitrary homogeneous ideal and give a relationship between geometric vertex decomposition of a polarization and elementary G‐biliaison that is analogous to our result on vertex decomposition and basic double G‐linkage.
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This content will become publicly available on May 8, 2026
The other ADM
Abstract In the peculiar manner by which physicists reckon descent, this article is by a ‘child’ and ‘grandchild’ of the late Stanley Deser. We begin by sharing reminiscences of Stanley from over 40 years. Then we turn to a problem which was dear to his heart: the prospect that gravity might nonperturbatively screen its own ultraviolet divergences and those of other theories. After reviewing the original 1960 work by ADM, we describe a cosmological analogue of the problem and then begin the process of implementing it in gravity plus QED.
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- Award ID(s):
- 2207514
- PAR ID:
- 10617551
- Publisher / Repository:
- Journal of Physics A
- Date Published:
- Journal Name:
- Journal of Physics A: Mathematical and Theoretical
- Volume:
- 58
- Issue:
- 19
- ISSN:
- 1751-8113
- Page Range / eLocation ID:
- 195401
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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