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Convexit\'e holomorphe du rev\^etement de Malcev d'apr\`es S. Leroy

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arxiv 0809.0920 v1 pith:SJYIH5FO submitted 2008-09-05 math.AG math.CV

Benoît Claudon (IECN) This is my paper · ORCID
classification math.AGmath.CV
keywords leroycaseahleralbaneseattackconjectureconstructedconvexit
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In these notes, we present the strategy employed by S. Leroy to attack the nilpotent case of the Shafarevich conjecture. The projective case was treated in a paper of L. Katzarkov but Leroy's proof is largely independant and works in the K\"ahler setting as well. It is entirely based on the higher Albanese manifolds constructed by R. Hain.

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  1. On the holomorphic convexity of nilpotent coverings over compact K\"ahler surfaces

    math.CV 2024-11 conditional novelty 6.0 of 10

    Virtually nilpotent intermediate coverings of compact Kähler surfaces without two ends are holomorphically convex, and Malcev coverings of Kähler manifolds have at most one end.

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