Give a resriction to ensure a surgery of a balanced manifold is still balanced.
In the following essay
L.Alessandrini & G.Bassanelli, Smooth proper modifications of compact Kahler manifolds, Proc. Internat. Workshop on Complex Analysis (Wuppertal 1990), Complex Analysis, Aspects of Mathatics E, Vol. 17, Vieweg, Germany, 1991.
we know that if f: M $\rightarrow $ N is a modification, M is balanced, then N is balanced too.
I'm wondering if the condition is changed from modificaion to surgery, can it still be true?
Let us make it clear here.Surgery is defined in the page 52 of Kodaira's"Complex manifolds and deformations complex structures". Modification is defined on the page 236 of GTM213.