5 papers
Rigidity of Pseudoconvex Neighborhoods and Ohsawa--Takegoshi Extension
Takayuki Koike, Masakazu Takakura
Let be a holomorphic section of a holomorphic submersion with one-dimensional fibers over a connected compact complex manifold. Assuming that its normal bundle is unitary flat,…
Pluripotential geometry on semi-positive effective divisors of numerical dimension one
Takayuki Koike
We study the complex-analytic geometry of semi-positive holomorphic line bundles on compact Kähler manifolds. In one of our main results, for a -effective line bundle s…
On neighborhoods of projective space bundles over elliptic curves
Takayuki Koike, Laurent Stolovitch
We give conditions ensuring that a neighborhood of an embedded projective space bundle over an elliptic curve is holomorphically equivalent to a neighborhood of the zero section of…
Formal principle for line bundles on neighborhoods of an analytic subset of a compact Kähler manifold
Takayuki Koike
We investigate the formal principle for holomorphic line bundles on neighborhoods of an analytic subset of a complex manifold mainly in the case where it can be realized as an open…
Neighborhood of a rational curve with an ordinary cusp
Takayuki Koike, Takato Uehara
We investigate complex analytic properties of a neighborhood of a reduced rational curve with an ordinary cusp embedded in a non-singular complex surface whose self-intersection nu…