Archiv der Mathematik

, Volume 112, Issue 1, pp 61–69 | Cite as

A relative completeness theorem

  • Viorel VâjâituEmail author


We prove a relative n-completeness theorem asserting that a complex space Y that fibers over a complex space X of dimension less than n is n-complete provided that Y admits a continuous exhaustion function that is strictly plurisubharmonic along fibers. We apply it to a particular case related to Skoda’s conjecture.


q-Convex function Plurisubharmonic function Skoda’s conjecture 

Mathematics Subject Classification

32F10 32U05 


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Laboratoire Paul PainlevéUniversité des Sciences et Technologies de Lille 1Villeneuve d’Ascq CedexFrance

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