# Coleff-Herrera currents, duality, and noetherian operators

Bulletin de la Société Mathématique de France (2011)

- Volume: 139, Issue: 4, page 535-554
- ISSN: 0037-9484

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topAndersson, Mats. "Coleff-Herrera currents, duality, and noetherian operators." Bulletin de la Société Mathématique de France 139.4 (2011): 535-554. <http://eudml.org/doc/272556>.

@article{Andersson2011,

abstract = {Let $\{\mathcal \{I\}\}$ be a coherent subsheaf of a locally free sheaf $\{\mathcal \{O\}\}(E_0)$ and suppose that $\{\mathcal \{F\}\}=\{\mathcal \{O\}\}(E_0)/\{\mathcal \{I\}\}$ has pure codimension. Starting with a residue current $R$ obtained from a locally free resolution of $\{\mathcal \{F\}\}$ we construct a vector-valued Coleff-Herrera current $\mu $ with support on the variety associated to $\{\mathcal \{F\}\}$ such that $\phi $ is in $\{\mathcal \{I\}\}$ if and only if $\mu \phi =0$. Such a current $\mu $ can also be derived algebraically from a fundamental theorem of Roos about the bidualizing functor, and the relation between these two approaches is discussed. By a construction due to Björk one gets Noetherian operators for $\{\mathcal \{I\}\}$ from the current $\mu $. The current $R$ also provides an explicit realization of the Dickenstein-Sessa decomposition and other related canonical isomorphisms.},

author = {Andersson, Mats},

journal = {Bulletin de la Société Mathématique de France},

keywords = {Coleff-Herrera current; duality; noetherian operators; residue current},

language = {eng},

number = {4},

pages = {535-554},

publisher = {Société mathématique de France},

title = {Coleff-Herrera currents, duality, and noetherian operators},

url = {http://eudml.org/doc/272556},

volume = {139},

year = {2011},

}

TY - JOUR

AU - Andersson, Mats

TI - Coleff-Herrera currents, duality, and noetherian operators

JO - Bulletin de la Société Mathématique de France

PY - 2011

PB - Société mathématique de France

VL - 139

IS - 4

SP - 535

EP - 554

AB - Let ${\mathcal {I}}$ be a coherent subsheaf of a locally free sheaf ${\mathcal {O}}(E_0)$ and suppose that ${\mathcal {F}}={\mathcal {O}}(E_0)/{\mathcal {I}}$ has pure codimension. Starting with a residue current $R$ obtained from a locally free resolution of ${\mathcal {F}}$ we construct a vector-valued Coleff-Herrera current $\mu $ with support on the variety associated to ${\mathcal {F}}$ such that $\phi $ is in ${\mathcal {I}}$ if and only if $\mu \phi =0$. Such a current $\mu $ can also be derived algebraically from a fundamental theorem of Roos about the bidualizing functor, and the relation between these two approaches is discussed. By a construction due to Björk one gets Noetherian operators for ${\mathcal {I}}$ from the current $\mu $. The current $R$ also provides an explicit realization of the Dickenstein-Sessa decomposition and other related canonical isomorphisms.

LA - eng

KW - Coleff-Herrera current; duality; noetherian operators; residue current

UR - http://eudml.org/doc/272556

ER -

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