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# Residue currents on analytic spaces

Richard Lärkäng (Institutionen för matematiska vetenskaper, matematik)
Göteborg2010. - 60 s.
[Licentiatavhandling]

This thesis concerns residue currents on analytic spaces.

In the first paper, we construct Coleff-Herrera products and Bochner-Martinelli type currents associated with a weakly holomorphic mapping, and show that these currents satisfy well-known properties from the strongly holomorphic case. This includes the transformation law, the Poincaré-Lelong formula and the equivalence of the Coleff-Herrera product and the Bochner-Martinelli current associated with a complete intersection of weakly holomorphic functions.

In the second paper, we discuss the duality theorem on singular varieties. In the case of a complex manifold, the duality theorem, proven by Dickenstein-Sessa and Passare, says that the annihilator of the Coleff-Herrera product associated with a complete intersection $f$ equals the ideal generated by $f$. We give sufficient and in many cases necessary conditions in terms of certain singularity subvarieties of the sheaf $\mathcal{O}_Z$ for when the duality theorem holds on a singular variety $Z$.

Nyckelord: analytic spaces, weakly holomorphic functions, residue currents, Coleff-Herrera products, the duality theorem

CPL Pubid: 121457

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# Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

# Examination

Datum: 2010-06-09
Tid: 10:00
Lokal: Pascal, Matematiska vetenskaper, Chalmers tvärgata 3, Göteborg
Opponent: Prof. Alain Yger, Université Bordeaux 1, Frankrike