A proper modification of a Kähler manifold is not necessarily Kähler. The authors prove that, instead, the classical example of Hironaka of a non-Kähler proper modification of P3, biholomorphic outside the curve with equations y2 = x2 +x3 and z = 0 in P3, is balanced. Recall that a compact manifold is balanced if it admits a Hermitian metric whose Kähler form is co-closed. The proof relies on the following technical result: The only positive (p, p) current T satisfying (de-debar)T = 0, whose support has zero Hausdorff 2p-measure, is T = 0.
A balanced proper modification of P3 / Alessandrini, Lucia; Bassanelli, Giovanni. - In: COMMENTARII MATHEMATICI HELVETICI. - ISSN 0010-2571. - 66:(1991), pp. 505-511. [10.5169/seals-50412]
A balanced proper modification of P3
ALESSANDRINI, Lucia;BASSANELLI, Giovanni
1991-01-01
Abstract
A proper modification of a Kähler manifold is not necessarily Kähler. The authors prove that, instead, the classical example of Hironaka of a non-Kähler proper modification of P3, biholomorphic outside the curve with equations y2 = x2 +x3 and z = 0 in P3, is balanced. Recall that a compact manifold is balanced if it admits a Hermitian metric whose Kähler form is co-closed. The proof relies on the following technical result: The only positive (p, p) current T satisfying (de-debar)T = 0, whose support has zero Hausdorff 2p-measure, is T = 0.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.