Published May 2013
| public
Journal Article
Strong nonnegativity and sums of squares on real varieties
- Creators
- Omar, Mohamed
- Osserman, Brian
Abstract
Motivated by scheme theory, we introduce strong nonnegativity on real varieties, which has the property that a sum of squares is strongly nonnegative. We show that this algebraic property is equivalent to nonnegativity for nonsingular real varieties. Moreover, for singular varieties, we re-prove and generalize obstructions of Gouveia and Netzer to the convergence of the theta body hierarchy of convex bodies approximating the convex hull of a real variety.
Additional Information
© 2012 Elsevier B.V. Received 1 April 2012; Received in revised form 28 July 2012; Available online 23 September 2012. Communicated by S. Kovacs. We would like to thank Rekha Thomas and João Gouveia for helpful conversations. In particular, Examples 3.9 and 3.10 were found in consultation with them. We would also like to thank the referees for thorough readings and helpful comments. The first author was partially supported by NSERC PGS-D 281174 and NSF grant DMS-0914107.Additional details
- Eprint ID
- 37209
- DOI
- 10.1016/j.jpaa.2012.09.007
- Resolver ID
- CaltechAUTHORS:20130228-125558021
- PGS-D 281174
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- DMS-0914107
- NSF
- Created
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2013-03-01Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field