7 papers · 1 filter
Opers on transversely holomorphic foliations
Indranil Biswas, Sorin Dumitrescu
For real codimension two smooth foliations, we study the transversely complex structures, transversely complex projective structures and transverse opers associated to the foliatio…
Non-Kähler Calabi-Yau manifolds and holomorphic geometric structures
Indranil Biswas, Sorin Dumitrescu
We study holomorphic geometric structures on non-Kähler compact complex manifolds with trivial canonical line bundle. For Vaisman Calabi-Yau manifolds we prove that all holomorphic…
Turbulent holomorphic foliations on compact complex tori and transversely holomorphic Cartan geometry
Indranil Biswas, Sorin Dumitrescu
We define a class of nonsingular holomorphic foliations on compact complex tori which generalizes (in higher codimension) the turbulent foliations of codimension one constructed by…
Holomorphic foliations with no transversely projective structure
Indranil Biswas, Sorin Dumitrescu
We prove that on the product of two elliptic curves a generic nonsingular turbulent foliation does not admit any transversely projective structure.
Holomorphic geometric structures on Oeljeklaus-Toma manifolds
Indranil Biswas, Sorin Dumitrescu
We prove that any holomorphic geometric structure of affine type on an Oeljeklaus- Toma manifold is locally homogeneous. For locally conformal Kähler Oeljeklaus-Toma manifolds we p…
Principal bundles with holomorphic connections over a Kaehler Calabi-Yau manifold
Indranil Biswas, Sorin Dumitrescu
We prove that any holomorphic vector bundle admitting a holomorphic connection, over a compact Kähler Calabi-Yau manifold, also admits a flat holomorphic connection. This addresses…
On the monodromy of holomorphic differential systems
Indranil Biswas, Sorin Dumitrescu, Lynn Heller +2
First we survey and explain the strategy of some recent results that construct holomorphic -differential systems over some Riemann surfaces of genus…