Dan Popovici

activity

20242026

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6 papers · 1 filter

math.AG2025

Generalised Hermite-Einstein Fibre Metrics and Slope Stability for Holomorphic Vector Bundles

Dan Popovici

Let $X$ be a compact complex manifold of dimension $n$ and let $m$ be a positive integer with $m \leq n$ . Assume that $X$ admits a Kähler metric $ω$ and a weakly positive, $\partial…

math.DG2025

Properties of Holomorphic $p$ -Contact Manifolds

Hisashi Kasuya, Dan Popovici, Luis Ugarte

We continue the study of compact holomorphic $p$ -contact manifolds $X$ that we introduced recently by expanding the discussion to include non-Kähler hyperbolicity issues and a diff…

math.DG2025

Holomorphic $p$ -Contact and $s$ -Symplectic Line Bundles

Kyle Broder, Dan Popovici

We generalise the notions of scalar-valued holomorphic $p$ -contact and $s$ -symplectic structures introduced recently on compact complex manifolds by the second-named author jointly…

math.DG2025

$m$ -Pseudo-effectivity and a Monge-Ampère-Type Equation for Forms of Positive Degree

Sławomir Dinew, Dan Popovici

Given an $n$ -dimensional compact Kähler manifold, we continue our study of $m$ -positivity in two ways. We first propose generalisations of the notions of pseudo-effective and big B…

math.DG2025

$m$ -Positivity and Regularisation

Sławomir Dinew, Dan Popovici

Starting from the notion of $m$ -plurisubharmonic function introduced recently by Dieu and studied, in particular, by Harvey and Lawson, we consider $m$ -(semi-)positive $(1, 1)$ -cu…

math.DG2025

Higher-Degree Holomorphic Contact Structures

Hisashi Kasuya, Dan Popovici, Luis Ugarte

We introduce the classes of holomorphic $p$ -contact manifolds and holomorphic $s$ -symplectic manifolds that generalise the classical holomorphic contact and holomorphic symplectic…

Generalised Hermite-Einstein Fibre Metrics and Slope Stability for Holomorphic Vector Bundles

Properties of Holomorphic p-Contact Manifolds

Holomorphic p-Contact and s-Symplectic Line Bundles

m-Pseudo-effectivity and a Monge-Ampère-Type Equation for Forms of Positive Degree

m-Positivity and Regularisation

Higher-Degree Holomorphic Contact Structures

Properties of Holomorphic $p$ -Contact Manifolds

Holomorphic $p$ -Contact and $s$ -Symplectic Line Bundles

$m$ -Pseudo-effectivity and a Monge-Ampère-Type Equation for Forms of Positive Degree

$m$ -Positivity and Regularisation