arXiv subjects

Vlad Marchidanu

Publications and source records attributed to Vlad Marchidanu.

3 recordsLinked to original sources

arXiv2026

Holomorphic tensors on products of algebraic cones

We study the product $C$ of two algebraic cones equipped with algebraic structures given by contractions. First we show that any holomorphic tensor on a quotient of $C$ by a group containing a contraction on both factors is invariant under the Zariski closure of this contraction when the factors have dimension $\geq 2$. We then give an explicit embedding of the cone of a Sasaki manifold to a normal variety. Using it and the result on algebraic cones, we prove that any holomorphic tensor on the product of two Sasaki manifolds is invariant under the flows of the Reeb fields.

math.AG↗

arXiv2025

An Aubin-Yau theorem for transversally K\"ahler foliations

Transversally K\"ahler foliations are a generalisation of K\"ahler manifolds, appearing naturally in the complex non-K\"ahler setting. We give a self-contained proof of how the classical methods used in the proof of the Aubin-Yau theorem adapt to the transversally K\"ahler case under the homological orientability condition. We apply this result to obtain a new, simpler proof of the already known Vaisman Aubin-Yau theorem.

math.DG↗

arXiv2023

Complex structures on the product of two Sasakian manifolds

A Sasakian manifold is a Riemannian manifold whose metric cone admits a certain K\"ahler structure which behaves well under homotheties. We show that the product of two compact Sasakian manifolds admits a family of complex structures indexed by a complex nonreal parameter, none of whose members admits any compatible locally conformally K\"ahler metrics if both Sasakian manifolds are of dimension greater than $1$. We compare this family with another family of complex structures which has been studied in the literature. We compute the Dolbeault cohomology groups of these products of compact Sasakian manifolds.

math.DG↗