Holomorphic Functions on Bundles Over Annuli
| dc.creator | Zaffran, Dan | |
| dc.date | 2008-10-10 | |
| dc.date.accessioned | 2026-07-07T10:09:07Z | |
| dc.date.available | 2026-07-07T10:09:07Z | |
| dc.description | 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. Then E_m(D,M) is defined as the flat bundle over the annulus of modulus m>0, with fiber D, and monodromy f. We show that the function theory on E_m(D,M) depends nontrivially 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 π^2, where r(M) denotes the 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 Siu Y.-T. | |
| dc.identifier | https://arxiv.org/abs/0810.1817 | |
| dc.identifier | http://arxiv.org/abs/0810.1817 | |
| dc.identifier | Math. Ann. 341 (2008), no. 4, 717--733 | |
| dc.identifier | doi:10.1007/s00208-007-0201-4 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171224 | |
| dc.subject | Complex Variables | |
| dc.title | Holomorphic Functions on Bundles Over Annuli | |
| dc.type | text |