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Mean curvature of direct image bundles
Kuang-Ru Wu
https://arxiv.org/abs/2508.00820 https://arxiv.org/pdf/2508.00820

Mean curvature of direct image bundles
Let $E\to X$ be a vector bundle of rank $r$ over a compact complex manifold $X$ of dimension $n$. It is known that if the line bundle $O_{P(E^*)}(1)$ over the projectivized bundle $P(E^*)$ is positive, then $E\otimes \det E$ is Nakano positive by the work of Berndtsson. In this paper, we give a subharmonic analogue. Let $p:P(E^*)\to X$ be the projection and $α$ be a Kähler form on $X$. If the line bundle $O_{P(E^*)}(1)$ admits a metric $h$ with curvature $Θ$ positive on every fiber and $Θ^r…

The Iarrobino scheme: a self-dual analogue of the Hilbert scheme of points
Joachim Jelisiejew
https://arxiv.org/abs/2508.21705 https://arxiv.org/pdf/2508.2…

The Iarrobino scheme: a self-dual analogue of the Hilbert scheme of points
For a fixed quasi-projective scheme $X$ we introduce a self-dual analogue of ${\mathrm{Hilb}}_d(X)$ which we call the Iarrobino scheme of $X$. It is a fine moduli space of oriented Gorenstein zero-dimensional subschemes of $X$ together with some additional data (a self-dual filtration) which is vacuous over a big open set but non-trivial over the compactification. Via the link between Hilbert schemes and varieties of commuting matrices, Iarrobino schemes correspond to commuting symmetric matric…