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

	Text Ballico-Ventura2020_Article_LabelsOfRealProjectiveVarietie.pdf - Published Version Restricted to registered users only Available under License Publisher holds Copyright. Download (392kB)
Preview	Text 1909.11170.pdf - Accepted Version Available under License Publisher holds Copyright. Download (263kB) | Preview

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.

Interest & Impact

Downloads

14 since deposited on 10 Feb 2021
2 in the past 12 months

Citations

5 Citations in Web of Science ®
6 Citations in Scopus

Search

in Google Scholar™

Services

Actions (login required)

Edit item

Actions (login required)

Edit item