Bonacho dos Anjos Henriques, I. and Varbaro, M. (2016) Test, multiplier and invariant ideals. Advances in Mathematics, 287. pp. 704-732. ISSN 1090-2082
Abstract
This paper gives an explicit formula for the multiplier ideals, and consequently for the log canonical thresholds, of any GL(V ) × GL(W)-invariant ideal in S = Sym(V ⊗ W∗), where V and W are vector spaces over a field of characteristic 0. This characterization is done in terms of a polytope constructed from the set of Young diagrams corresponding to the Schur modules generating the ideal. Our approach consists in computing the test ideals of some invariant ideals of S in positive characteristic: Namely, we compute the test ideals (and so the F-pure thresholds) of any sum of products of determinantal ideals. Not all the invariant ideals are as the latter (not even in characteristic 0), but they are up to integral closure, and this is enough to reach our goals. The results concerning the test ideals are obtained as a consequence of general results holding true in a special situation. Within such framework fall determinantal objects of a generic matrix, as well as of a symmetric matrix and of a skew-symmetric one. (Monomial ideals also fall in this framework, thus we recover Howald’s formula for their multiplier ideals and, more generally, Hara–Yoshida’s formula for their test ideals.) In the proof, we introduce the notion of “floating test ideals”, a property that in a sense is satisfied by ideals.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015 Elsevier Inc. This is an author produced version of a paper subsequently published in Advances in Mathematics. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/) |
Keywords: | Test ideals; Multiplier ideals; Invariant ideals; Determinantal ideals; Pfaffian ideals; F-pure thresholds; Log canonical thresholds |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Medicine, Dentistry and Health (Sheffield) > School of Health and Related Research (Sheffield) > ScHARR - Sheffield Centre for Health and Related Research |
Funding Information: | Funder Grant number ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL (EPSRC) EP/J005436/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 20 Apr 2016 10:13 |
Last Modified: | 30 Nov 2016 10:56 |
Published Version: | http://dx.doi.org/10.1016/j.aim.2015.09.028 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.aim.2015.09.028 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:97438 |