Journal article
Conormal spaces and Whitney stratifications
- Abstract:
- We describe a new algorithm for computing Whitney stratifications of complex projective varieties. The main ingredients are (a) an algebraic criterion, due to Lê and Teissier, which reformulates Whitney regularity in terms of conormal spaces and maps, and (b) a new interpretation of this conormal criterion via ideal saturations, which can be practically implemented on a computer. We show that this algorithm improves upon the existing state of the art by several orders of magnitude, even for relatively small input varieties. En route, we introduce related algorithms for efficiently stratifying affine varieties, flags on a given variety, and algebraic maps.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Publisher copy:
- 10.1007/s10208-022-09574-8
Authors
- Publisher:
- Springer
- Journal:
- Foundations of Computational Mathematics More from this journal
- Volume:
- 23
- Pages:
- 1745-1780
- Publication date:
- 2022-06-14
- Acceptance date:
- 2022-04-25
- DOI:
- EISSN:
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1615-3383
- ISSN:
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1615-3375
- Language:
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English
- Keywords:
- Pubs id:
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1255263
- Local pid:
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pubs:1255263
- Deposit date:
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2022-05-01
- ARK identifier:
Terms of use
- Copyright holder:
- Helmer and Nanda
- Copyright date:
- 2022
- Rights statement:
- Copyright © 2022 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
- Notes:
- A correction to this article is available online from Springer at: 10.1007/s10208-022-09602-7
- Licence:
- CC Attribution (CC BY)
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