English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider a family E_m(D,M) of holomorphic bundles constructed as follows:to any given M in GL_n(Z), we associate a "multiplicative automorphism" f of(C*)^n. Now let D be a f-invariant Stein Reinhardt domain in (C*)^n. ThenE_m(D,M) is defined as the flat bundle over the annulus of modulus m>0, withfiber D, and monodromy f. We show that the function theory on E_m(D,M) dependsnontrivially on the parameters m, M and D. Our main result is that  E_m(D,M) is Stein if and only if m log(r(M)) <= 2 \pi^2, where r(M) denotesthe max of the spectral radii of M and its inverse. As corollaries, we: --obtain a classification result for Reinhardt domains in all dimensions; --establish a similarity between two known counterexamples to a question of J.-P.Serre; -- suggest a potential reformulation of a disproved conjecture of SiuY.-T.

Holomorphic Functions on Bundles Over Annuli