Decomposition of residue currents

Andersson, Mats; Wulcan, Elizabeth

doi:10.1515/crelle.2010.004

Cited by 43 publications

(128 citation statements)

References 9 publications

Supporting

Mentioning

128

Contrasting

Order By: Relevance

“…Thus µ f has the SEP and so µ f ∈ CH Z f . This proof is inspired by a forthcoming joint paper, [2], with Elizabeth Wulcan.…”

Section: The Coleff-herrera Productmentioning

confidence: 99%

Uniqueness and factorization of Coleff-Herrera currents

Andersson¹

2010

Annales De La Faculté Des Sciences De Toulouse : Mathématiques

Self Cite

View full text Add to dashboard Cite

Abstract. We prove a uniqueness result for Coleff-Herrera currents which in particular means that if f = (f 1 , . . . , f m ) defines a complete intersection, then the classical Coleff-Herrera product associated to f is the unique Coleff-Herrera current that is cohomologous to 1 with respect to the operator δ f −∂, where δ f is interior multiplication with f . From the uniqueness result we deduce that any Coleff-Herrera current on a variety Z is a finite sum of products of residue currents with support on Z and holomorphic forms.

show abstract

“…Thus µ f has the SEP and so µ f ∈ CH Z f . This proof is inspired by a forthcoming joint paper, [2], with Elizabeth Wulcan.…”

Section: The Coleff-herrera Productmentioning

confidence: 99%

Uniqueness and factorization of Coleff-Herrera currents

Andersson¹

2010

Annales De La Faculté Des Sciences De Toulouse : Mathématiques

Self Cite

View full text Add to dashboard Cite

show abstract

“…They can both be used (see [3,7]) to materialize the residual obstruction for the exactness of the generically exact Koszul complex…”

Section: Averaging Vogel Residue Currentsmentioning

confidence: 99%

“…We still use analytic continuation, but this time respect to a single auxiliary complex parameter λ instead of several. Such an approach was introduced in [9,27], then extensively developed (after being interpreted within the frame of holomorphic hermitian bundles) in [3,4,6,7]. It is based on an averaging procedure.…”

mentioning

confidence: 99%

Averaging Residue Currents and the Stückrad–Vogel Algorithm

Yger

2012

The Mathematical Legacy of Leon Ehrenpreis

View full text Add to dashboard Cite

Trace formulas (Lagrange, Jacobi-Kronecker, Bergman-Weil) play a key role in division problems in analytic or algebraic geometry (including arithmetic aspects, see for example [10]). Unfortunately, they usually hold within the restricted frame of complete intersections. Besides the fact that it allows to carry local or semi global analytic problems to a global geometric setting (think about Crofton's formula), averaging the Cauchy kernel (from C n \{z 1 . . . z n = 0} ⊂ P n (C)), in order to get the Bochner-Martinelli kernel (in C n+1 \ {0} ⊂ P n+1 (C) = C n+1 ∪ P n (C)), leads to the construction of explicit candidates for the realization of Grothendieck's duality, namely BM residue currents ([27, 3, 6]), extending thus the cohomological incarnation of duality which appears in the complete intersection or Cohen-Macaulay cases. We will recall here such constructions and, in parallel, suggest how far one could take advantage of the multiplicative inductive construction introduced in [13] by N. Coleff and M. Herrera, by relating it to the Stückrad-Vogel algorithm developed in ([30], [31], [8]) towards improper intersection theory. Results presented here were initiated all along my long term collaboration with Carlos Berenstein. To both of us, the mathematical work of Leon Ehrenpreis certainly remained a constant and how much stimulating source of inspiration. This presentation relies also deeply on my collaboration with M. Andersson, H. Samuelsson and E. Wulcan in Göteborg, through the past years.

show abstract

“…In [6] the class of pseudomeromorphic currents is introduced. The definition is modeled on the residue currents that appear in various works such as [2] and [21]; a current is pseudomeromorphic if it can be written as a locally finite sum of push-forwards under holomorphic modifications of currents of the simple form…”

Section: Restrictions Of Currents and The Standard Extension Propertymentioning

confidence: 99%

“…Thus R and R I are pseudomeromorphic in the sense of [6] and so it makes sense to take restrictions of them to subvarieties of their support, see Section 2.1.…”

Section: Annales De L'institut Fouriermentioning

confidence: 99%