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Explicit Serre duality on complex spaces

Jean Ruppenthal ; Håkan Samuelsson (Institutionen för matematiska vetenskaper, matematik) ; Elizabeth Wulcan (Institutionen för matematiska vetenskaper, matematik)
Advances in Mathematics (0001-8708). Vol. 305 (2017), p. 1320-1355.
[Artikel, refereegranskad vetenskaplig]

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 n-dimensional paracompact complex space X. At the core of the paper is the introduction of concrete fine sheaves $A^{n,q}_X$ of certain currents on X of bidegree (n,q), such that the corresponding Dolbeault complex becomes, in a certain sense, a dualizing complex. In particular, if X is Cohen-Macaulay (e.g., Gorenstein or a complete intersection) then this Dolbeault complex becomes an explicit fine resolution of the Grothendieck dualizing sheaf.



Denna post skapades 2014-12-04. Senast ändrad 2017-08-18.
CPL Pubid: 207342

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik
Matematisk analys
Geometri

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