Victor Vuletescu

Examples of non-trivial rank in locally conformal Kähler geometry

We consider locally conformal Kähler geometry as an equivariant, homothetic Kähler geometry (K, Γ). We show that the de Rham class of the Lee form can be naturally identified with the homomorphism projecting Γ to its dilation factors, thus completing the description of locally conformal Kähler geometry in this equivariant setting. The rank rM of a locally conformal Kähler manifold is the rank of the image of this homomorphism. Using algebraic number theory, we show that rM is non-trivial, providing explicit examples of locally conformal Kähler manifolds with

Flat affine subvarieties in Oeljeklaus–Toma manifolds

{1\nless{\text{\upshape \rmfamily r}_{M}}\nless b_1}

Spin(9) geometry of the octonionic Hopf fibration

. As far as we know, these are the first examples of this kind. Moreover, we prove that locally conformal Kähler Oeljeklaus-Toma manifolds have either rM = b1 or rM = b1/2.

Clifford systems in octonionic geometry

A locally conformally Kahler (LCK) manifold is a complex manifold with a Kahler structure on its covering and the deck transform group acting on it by holomorphic homotheties. One could think of an LCK manifold as of a complex manifold with a Kahler form taking values in a local system

LCK metrics on Oeljeklaus-Toma manifolds versus Kronecker's theorem

L

Elliptic Gauss sums and applications to point counting

, called the conformal weight bundle. The

A restriction theorem for torsion-free sheaves on some elliptic manifolds

L

Oeljeklaus-Toma manifolds and locally conformally Kahler metrics. A state of the art

-valued cohomology of