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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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The $L^2$ $\bar \partial$-method, weak Lefschetz theorems, and the topology of Kähler manifolds
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by Terrence Napier and Mohan Ramachandran PDF
J. Amer. Math. Soc. 11 (1998), 375-396 Request permission


A new approach to Nori’s weak Lefschetz theorem is described. The new approach, which involves the $\bar \partial$-method, avoids moving arguments and gives much stronger results. In particular, it is proved that if $X$ and $Y$ are connected smooth projective varieties of positive dimension and $f : Y \rightarrow X$ is a holomorphic immersion with ample normal bundle, then the image of $\pi _1(Y)$ in $\pi _1(X)$ is of finite index. This result is obtained as a consequence of a direct generalization of Nori’s theorem. The second part concerns a new approach to the theorem of Burns which states that a quotient of the unit ball in $\Bbb C ^n$ ($n\geq 3$) by a discrete group of automorphisms which has a strongly pseudoconvex boundary component has only finitely many ends. The following generalization is obtained. If a complete Hermitian manifold $X$ of dimension $n\geq 3$ has a strongly pseudoconvex end $E$ and $\text {Ricci} (X) \leq -C$ for some positive constant $C$, then, away from $E$, $X$ has finite volume.
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Additional Information
  • Terrence Napier
  • Affiliation: Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015
  • Email:
  • Mohan Ramachandran
  • Affiliation: Department of Mathematics, SUNY at Buffalo, Buffalo, New York 14214
  • Email:
  • Received by editor(s): July 8, 1997
  • Received by editor(s) in revised form: November 4, 1997
  • Additional Notes: The authors’ research was partially supported by NSF grants DMS9411154 (T.N.) and DMS9626169 (M.R.).
  • © Copyright 1998 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 11 (1998), 375-396
  • MSC (1991): Primary 14E20, 32C10, 32C17
  • DOI:
  • MathSciNet review: 1477601