In algebraic geometry weighted projective spaces (WPS) are very popular ! In algebraic topology , WLS have been (cohomologically at least) studied. Roughly speaking , a WPS is almost covered by WLS's (as open subsets). As far as I know, there is no PUBLISHED study or use of WLS, in ALGEBRAIC GEOMETRY. Is it true ?
This is a propaganda for weighted lens spaces (WLS) ! Since nobody seems to be interested in the subject, let me "recall" fundamental facts about them. They are strongly linked to weighted projective spaces (WPS).T.Kawasaki used essentially WLS to compute the integral cohomology ring of WPS . WLS's project naturally on WPS's, since they are defined by the same weighted action of C* when restricted to q-roots of unity ( some fixed q). The open orbifolds-charts which cover a WPS are , except for the origin (a fixed point), WLS's ! Another link between WLS's and WPS's is that, roughly speaking, "a WLS is the complement of the null section of an orbibundle over a WPS". If all the weights divide q , then this is a line vector bundle. An interesting fact is that WLS's can be defined à la GROTHENDIECK (as a generalization of Proj : Proj is the particular case when "q is zero" !). Now,let me ask : what is written/published somewhere on algebraic WLS's ?