Header

UZH-Logo

Maintenance Infos

A wall-crossing formula for degrees of Real central projections


Okonek, Christian; Teleman, Andrei (2014). A wall-crossing formula for degrees of Real central projections. International Journal of Mathematics, 25(4):1450038.

Abstract

The main result is a wall-crossing formula for central projections defined on submanifolds of a Real projective space. Our formula gives the jump of the degree of such a projection when the center of the projection varies. The fact that the degree depends on the projection is a new phenomenon, specific to Real algebraic geometry. We illustrate this phenomenon in many interesting situations. The crucial assumption on the class of maps we consider is relative orientability, a condition which allows us to define a ℤ-valued degree map in a coherent way. We end the article with several examples, e.g. the pole placement map associated with a quotient, the Wronski map, and a new version of the Real subspace problem.

Abstract

The main result is a wall-crossing formula for central projections defined on submanifolds of a Real projective space. Our formula gives the jump of the degree of such a projection when the center of the projection varies. The fact that the degree depends on the projection is a new phenomenon, specific to Real algebraic geometry. We illustrate this phenomenon in many interesting situations. The crucial assumption on the class of maps we consider is relative orientability, a condition which allows us to define a ℤ-valued degree map in a coherent way. We end the article with several examples, e.g. the pole placement map associated with a quotient, the Wronski map, and a new version of the Real subspace problem.

Statistics

Citations

Dimensions.ai Metrics
2 citations in Web of Science®
2 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

2 downloads since deposited on 15 Oct 2014
0 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > General Mathematics
Language:English
Date:2014
Deposited On:15 Oct 2014 10:51
Last Modified:12 Nov 2023 02:40
Publisher:World Scientific Publishing
ISSN:0129-167X
OA Status:Closed
Publisher DOI:https://doi.org/10.1142/S0129167X14500384