Non-upper-semicontinuity of Algebraic Dimension for Families of Compact Complex Manifolds
نویسنده
چکیده
In this note we show that in a certain subfamily of the Kuranishi family of any half Inoue surface the algebraic dimensions of the fibers jump downwards at special points of the parameter space showing that the upper semi-continuity of algebraic dimensions in any sense does not hold in general for families of compact non-Kähler manifolds. In the Kähler case, the upper semi-continuity always holds true in a certain
منابع مشابه
Fractal Dimension of Graphs of Typical Continuous Functions on Manifolds
If M is a compact Riemannian manifold then we show that for typical continuous function defined on M, the upper box dimension of graph(f) is as big as possible and the lower box dimension of graph(f) is as small as possible.
متن کاملOn Stretch curvature of Finsler manifolds
In this paper, Finsler metrics with relatively non-negative (resp. non-positive), isotropic and constant stretch curvature are studied. In particular, it is showed that every compact Finsler manifold with relatively non-positive (resp. non-negative) stretch curvature is a Landsberg metric. Also, it is proved that every (α,β)-metric of non-zero constant flag curvature and non-zero relatively i...
متن کاملAlgebraic and symplectic Gromov-Witten invariants coincide
Gromov-Witten invariants “count” (pseudo-) holomorphic curves on algebraic or symplectic manifolds. This amounts to intersection theory on moduli spaces of such curves. Because in general these are non-compact, singular and not of “expected dimension”, a rigorous mathematical definition is far from trivial. For a reasonably large class of manifolds including Fano and Calabi-Yau manifolds this h...
متن کاملHolomorphic Affine Connections on Non-kähler Manifolds
Our aim here is to investigate the holomorphic geometric structures on compact complex manifolds which may not be Kähler. We prove that holomorphic geometric structures of affine type on compact Calabi-Yau manifolds with polystable tangent bundle (with respect to some Gauduchon metric on it) are locally homogeneous. In particular, if the geometric structure is rigid in Gromov’s sense, then the ...
متن کاملWarped product and quasi-Einstein metrics
Warped products provide a rich class of physically significant geometric objects. Warped product construction is an important method to produce a new metric with a base manifold and a fibre. We construct compact base manifolds with a positive scalar curvature which do not admit any non-trivial quasi-Einstein warped product, and non compact complete base manifolds which do not admit any non-triv...
متن کامل