Let M be a compact complex manifold and C in M be an irreducible curve such that M − C is Kähler. The paper studies the following problem: What are the cohomological obstructions on C so that M is Kähler? This problem is motivated by the fact that if M is a Moishezon manifold, then there exists an analytic subset Y of M with codimension n ≥ 2 such thatM −Y is Kähler. When dimM ≥ 3, the authors show that one and only one of the following cases can occur: (i) M is Kähler, (ii) C is the (1, 1)-component of a boundary, or (iii) C is part of the (1, 1)-component of a boundary. As a consequence, it is shown that if C is smooth with genus g satisfying NC|M · C > (dimM −1)(g −1), then M is Kähler. When M is a threefold, more precise results are given.

Compact complex threefold which are Kähler outside a smooth rational curve / Alessandrini, Lucia; Bassanelli, Giovanni. - In: MATHEMATISCHE NACHRICHTEN. - ISSN 0025-584X. - 207:(1999), pp. 21-59.

Compact complex threefold which are Kähler outside a smooth rational curve

ALESSANDRINI, Lucia;BASSANELLI, Giovanni
1999-01-01

Abstract

Let M be a compact complex manifold and C in M be an irreducible curve such that M − C is Kähler. The paper studies the following problem: What are the cohomological obstructions on C so that M is Kähler? This problem is motivated by the fact that if M is a Moishezon manifold, then there exists an analytic subset Y of M with codimension n ≥ 2 such thatM −Y is Kähler. When dimM ≥ 3, the authors show that one and only one of the following cases can occur: (i) M is Kähler, (ii) C is the (1, 1)-component of a boundary, or (iii) C is part of the (1, 1)-component of a boundary. As a consequence, it is shown that if C is smooth with genus g satisfying NC|M · C > (dimM −1)(g −1), then M is Kähler. When M is a threefold, more precise results are given.
1999
Compact complex threefold which are Kähler outside a smooth rational curve / Alessandrini, Lucia; Bassanelli, Giovanni. - In: MATHEMATISCHE NACHRICHTEN. - ISSN 0025-584X. - 207:(1999), pp. 21-59.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/1449725
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