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13.
Strongly pseudoconvex domains as subvarieties of complex manifolds
Drinovec-Drnovšek, Barbara ; Forstnerič, Franc, 1958-
V članku dokažemo eksistenčne in aproksimacijske rezultate za zaprte kompleksne podmnožice, ki so normalizirane s strogo psevdokonveksnimi Steinovimi območji. Potreben pogoj za obstoj takih podmnožic ...v kompleksni mnogoterosti ▫$X$▫ je izražen z Morsovimi indeksi in številom pozitivnih lastnih vrednosti Levijeve forme funkcije izčrpanja na ▫$X$▫. S primeri pokažemo, da pogojev v splošnem ne moremo omiliti. Dobimo optimalne rezultate za analitične podmnožice te oblike v komplementih kompaktnih kompleksnih podmnogoterosti z Griffiths pozitivnim normalnim svežnjem. V projektivnem primeru ti rezultati posplošijo klasične izreke Remmerta, Bishopa in Narasimhana o pravih holomorfnih preslikavah in vložitvah v ▫${\Bbb C}^n = {\Bbb P}^n \setminus {\BbbP}^{n-1}$▫.
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