Labels of real projective varieties

Ballico, Edoardo; Ventura, Emanuele (2020). Labels of real projective varieties. Bollettino dell'Unione Matematica Italiana, 13(2), pp. 257-273. Springer 10.1007/s40574-020-00215-y

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Let X be a complex projective variety defined over R. Recently, Bernardi and the first author introduced the notion of admissible rank with respect to X. This rank takes into account only decompositions that are stable under complex conjugation. Such a decomposition carries a label, i.e., a pair of integers recording the cardinality of its totally real part. We study basic properties of admissible ranks for varieties, along with special examples of curves; for instance, for rational normal curves admissible and complex ranks coincide. Along the way, we introduce the scheme theoretic version of admissible rank. Finally, analogously to the situation of real ranks, we analyze typical labels, i.e., those arising as labels of a full-dimensional Euclidean open set. We highlight similarities and differences with typical ranks.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Ventura, Emanuele

Subjects:

500 Science > 510 Mathematics

ISSN:

1972-6724

Publisher:

Springer

Funders:

[UNSPECIFIED] MIUR (INdAM) ; [UNSPECIFIED] GNSAGA (INdAM)

Language:

English

Submitter:

Sebastiano Don

Date Deposited:

10 Feb 2021 17:41

Last Modified:

11 Mar 2021 20:30

Publisher DOI:

10.1007/s40574-020-00215-y

ArXiv ID:

1909.11170

Uncontrolled Keywords:

Admissible rank, Typical labels, Semialgebraic sets, Real algebraic varieties

BORIS DOI:

10.48350/151276

URI:

https://boris.unibe.ch/id/eprint/151276

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