14 citations · 31 across the 9 of their papers we have counts for
9 papers
About top-degree - and -Dolbeault cohomologies of complex spaces with pseudoconvex boundary
Martin Sera
Let be a complex space of pure-dimension . For a pseudoconvex relatively compact domain in with -smooth boundary and embedded in a domain of the complex n…
On Lelong Numbers of Generalized Monge-Ampère Products
Martin Sera
We consider generalized (mixed) Monge-Ampère products of quasiplurisubharmonic functions (with and without analytic singularities) as they were introduced and studied in several ar…
On a mixed Monge-Ampère operator for quasiplurisubharmonic functions with analytic singularities
Richard Lärkäng, Martin Sera, Elizabeth Wulcan
We consider mixed Monge-Ampère products of quasiplurisubharmonic functions with analytic singularities, and show that such products may be regularized as explicit one parameter lim…
Chern forms of hermitian metrics with analytic singularities on vector bundles
Richard Lärkäng, Hossein Raufi, Martin Sera +1
We define Chern and Segre forms, or rather currents, associated with a Griffiths positive singular hermitian metric with analytic singularities on a holomorphic vector bundle $…
A smoothness criterion for complex spaces in terms of differential forms
Håkan Samuelsson Kalm, Martin Sera
For a reduced pure dimensional complex space , we show that if Barlet's recently introduced sheaf of holomorphic -forms or the sheaf of germs of weakly holomorphic $1…
Chern forms of singular metrics on vector bundles
Richard Lärkäng, Hossein Raufi, Jean Ruppenthal +1
We study singular hermitian metrics on holomorphic vector bundles, following Berndtsson-P{ă}un. Previous work by Raufi has shown that for such metrics, it is in general not possibl…
A generalization of Takegoshi's relative vanishing theorem
Martin Sera
We present a generalization of Takegoshi's relative version of the Grauert-Riemenschneider vanishing theorem. Under some natural assumptions, we extend Takegoshi's vanishing theore…
Modifications of torsion-free coherent analytic sheaves
Jean Ruppenthal, Martin Sera
We study the transformation of torsion-free coherent analytic sheaves under proper modifications. More precisely, we study direct images of inverse image sheaves, and torsion-free…
-Riemann-Roch for singular complex curves
Jean Ruppenthal, Martin Sera
We present a comprehensive -theory for the -operator on singular complex curves, including -versions of the Riemann-Roch theorem and some applications.