A complex n-dimensional manifold M is said to be Kähler if it carries a Hermitian metric whose Kähler form is d-closed. Analogously, M is called balanced if it has a Hermitian metric whose Kähler form w satisfies d(w)^(n−1) = 0. According to an example by H. Hironaka, the property of being Kähler does not persist in general when one takes modifications of M. The main result of this paper is that if ˜M is a smooth proper modification of M and if M is a compact, balanced manifold then ˜M is also balanced..
Smooth proper modifications of compact Kähler manifolds / Alessandrini, Lucia; Bassanelli, Giovanni. - E17:(1991), pp. 1-7. (Intervento presentato al convegno Complex Analysis. Dedicated to H. Grauert. Proceedings of the International Workshop Wuppertal 1990 tenutosi a WUPPERTAL nel February 12-16, 1991).
Smooth proper modifications of compact Kähler manifolds
ALESSANDRINI, Lucia;BASSANELLI, Giovanni
1991-01-01
Abstract
A complex n-dimensional manifold M is said to be Kähler if it carries a Hermitian metric whose Kähler form is d-closed. Analogously, M is called balanced if it has a Hermitian metric whose Kähler form w satisfies d(w)^(n−1) = 0. According to an example by H. Hironaka, the property of being Kähler does not persist in general when one takes modifications of M. The main result of this paper is that if ˜M is a smooth proper modification of M and if M is a compact, balanced manifold then ˜M is also balanced..I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
