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Explicit Serre duality on complex spaces

Håkan Samuelsson (Institutionen för matematiska vetenskaper, matematik) ; Elizabeth Wulcan (Institutionen för matematiska vetenskaper, matematik) ; Jean Ruppenthal
2014. - 28 s.
[Rapport]

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 associatd 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 is an explicit fine resolution of the Grothendieck dualizing sheaf.



Denna post skapades 2014-12-04. Senast ändrad 2016-04-28.
CPL Pubid: 207361

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik
Matematisk analys
Geometri

Chalmers infrastruktur