un 2 00 9 Blowing - up points on l . c . K . manifolds
نویسنده
چکیده
It is a classical result, due to F. Tricceri, that the blow-up of a manifold of locally conformally Kähler (l.c.K. for short) type at some point is again of l.c.K. type. However, the proof given in [5] is somehow unclear. We give a different argument to prove the result, using ”standard tricks” in algebraic geometry.
منابع مشابه
Topological invariants of generalized Kummer manifolds
Let L ⊆ C be a lattice and consider the compact complex torus XL = C/L. Let Γ 6 Aut(L) ∩ SL2m C be a (finite) group of automorphisms of L whose action on C is semifree (i.e., free away from 0). X L consists of finitely many isolated fixed points, so the orbifold XL/Γ has finitely many isolated singularities. We can resolve these singularities by ‘blowing up’ each of the singular points. In fact...
متن کاملun 2 00 2 Mukai flops and derived categories
Derived categories possibly give a new significant invariant for algebraic varieties. In particular, when the caninical line bundle is trivial, there are varieties which are not birationally equivalent, but have equivalent derived categories. The most typical example can be found in the original paper [Mu]. On the other hand, for such varieties, it is hoped that the birationally equivalence sho...
متن کاملGeneralized Calabi - Yau Manifolds and the Mirror of a Rigid Manifold
The Z manifold is a Calabi–Yau manifold with b 21 = 0. At first sight it seems to provide a counter example to the mirror hypothesis since its mirror would have b 11 = 0 and hence could not be Kähler. However by identifying the Z manifold with the Gepner model 1 9 we are able to ascribe a geometrical interpretation to the mirror, ˜ Z, as a certain seven-dimensional manifold. The mirror manifold...
متن کاملm at h . A G ] 1 4 A pr 2 00 9 CONIC - CONNECTED MANIFOLDS
We study a particular class of rationally connected manifolds, X ⊂ P , such that two general points x, x′ ∈ X may be joined by a conic contained in X. We prove that these manifolds are Fano, with b2 6 2. Moreover, a precise classification is obtained for b2 = 2. Complete intersections of high dimension with respect to their multi-degree provide examples for the case b2 = 1. The proof of the cla...
متن کاملBlowing up Kähler manifolds withconstant scalar curvature, II
In this paper we prove the existence of Kähler metrics of constant scalar curvature on the blow up at finitely many points of a compact manifold which already carries a Kähler constant scalar curvature metric. Necessary conditions of the number and locations of the blow up points are given. 1991 Math. Subject Classification: 58E11, 32C17.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009