Explicit Serre duality on complex spaces
Jean Ruppenthal, H{\aa}kan Samuelsson Kalm, Elizabeth Wulcan

TL;DR
This paper provides an explicit analytic realization and proof of Serre duality on reduced pure complex spaces using residue currents and integral formulas, introducing concrete sheaves that form a dualizing complex.
Contribution
It introduces concrete sheaves of currents that realize Serre duality explicitly and provides a new analytic proof applicable to all reduced pure complex spaces.
Findings
Constructs explicit fine sheaves of currents on complex spaces.
Shows the Dolbeault complex of these sheaves forms a dualizing complex.
Specializes to Cohen-Macaulay spaces where it resolves the dualizing sheaf.
Abstract
In this paper we use recently developed calculus of residue currents together with integral formulas to give a new explicit analytic realization, as well as a new analytic proof of Serre duality on any reduced pure -dimensional paracompact complex space . At the core of the paper is the introduction of concrete fine sheaves of certain currents on of bidegree , such that the Dolbeault complex becomes, in a certain sense, a dualizing complex. In particular, if is Cohen-Macaulay (e.g., Gorenstein or a complete intersection) then is an explicit fine resolution of the Grothendieck dualizing sheaf.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Algebraic structures and combinatorial models
