Browse issues
no. 1
Integral representation of moderate cohomology
Håkan Samuelsson Kalm1
1 Håkan Samuelsson Kalm, Department of Mathematical Sciences, Division of Algebra and Geometry, University of Gothenburg and Chalmers University of Technology, SE-412 96 Göteborg, Sweden
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 30 (2021) no. 1, pp. 117-137.

We make the classical Dickenstein–Sessa canonical representation in local moderate cohomology explicit by an integral formula. We also provide a similar representation of the higher local moderate cohomology groups.

Nous faisons la représentation canonique classique de Dickenstein–Sessa dans la cohomologie modérée locale explicite par une formule intégrale. Nous fournissons également une représentation similaire des groupes de cohomologie modérés locaux supérieurs.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1668
Classification: 32A26, 32A27, 32C25, 32C35
Keywords: moderate cohomology, integral representation, residue current, coherent ideal sheaf, complex space

Håkan Samuelsson Kalm 1

1 Håkan Samuelsson Kalm, Department of Mathematical Sciences, Division of Algebra and Geometry, University of Gothenburg and Chalmers University of Technology, SE-412 96 Göteborg, Sweden
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
@article{AFST_2021_6_30_1_117_0,
     author = {H\r{a}kan Samuelsson Kalm},
     title = {Integral representation of moderate cohomology},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {117--137},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 30},
     number = {1},
     year = {2021},
     doi = {10.5802/afst.1668},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1668/}
}
TY  - JOUR
AU  - Håkan Samuelsson Kalm
TI  - Integral representation of moderate cohomology
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2021
SP  - 117
EP  - 137
VL  - 30
IS  - 1
PB  - Université Paul Sabatier, Toulouse
UR  - https://afst.centre-mersenne.org/articles/10.5802/afst.1668/
DO  - 10.5802/afst.1668
LA  - en
ID  - AFST_2021_6_30_1_117_0
ER  - 
%0 Journal Article
%A Håkan Samuelsson Kalm
%T Integral representation of moderate cohomology
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2021
%P 117-137
%V 30
%N 1
%I Université Paul Sabatier, Toulouse
%U https://afst.centre-mersenne.org/articles/10.5802/afst.1668/
%R 10.5802/afst.1668
%G en
%F AFST_2021_6_30_1_117_0
Håkan Samuelsson Kalm. Integral representation of moderate cohomology. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 30 (2021) no. 1, pp. 117-137. doi : 10.5802/afst.1668. https://afst.centre-mersenne.org/articles/10.5802/afst.1668/

[1] Mats Andersson Integral representation with weights. I, Math. Ann., Volume 326 (2003) no. 1, pp. 1-18 | DOI | MR | Zbl

[2] Mats Andersson Residue currents and ideals of holomorphic functions, Bull. Sci. Math., Volume 128 (2004) no. 6, pp. 481-512 | DOI | MR | Zbl

[3] Mats Andersson Residues of holomorphic sections and Lelong currents, Ark. Mat., Volume 43 (2005) no. 2, pp. 201-219 | DOI | MR | Zbl

[4] Mats Andersson Integral representation with weights. II. Division and interpolation, Math. Z., Volume 254 (2006) no. 2, pp. 315-332 | DOI | MR | Zbl

[5] Mats Andersson Uniqueness and factorization of Coleff–Herrera currents, Ann. Fac. Sci. Toulouse, Math., Volume 18 (2009) no. 4, pp. 651-661 | DOI | Numdam | MR | Zbl

[6] Mats Andersson Coleff-Herrera currents, duality, and Noetherian operators, Bull. Soc. Math. Fr., Volume 139 (2011) no. 4, pp. 535-554 | DOI | Numdam | MR | Zbl

[7] Mats Andersson; Richard Lärkäng The ∂ ¯-equation on a non-reduced analytic space, Math. Ann., Volume 374 (2019) no. 1-2, pp. 553-599 | DOI | MR | Zbl

[8] Mats Andersson; Håkan Samuelsson Kalm A Dolbeault–Grothendieck lemma on complex spaces via Koppelman formulas, Invent. Math., Volume 190 (2012) no. 2, pp. 261-297 | DOI | MR | Zbl

[9] Mats Andersson; Elizabeth Wulcan Residue currents with prescribed annihilator ideals, Ann. Sci. Éc. Norm. Supér., Volume 40 (2007) no. 6, pp. 985-1007 | DOI | Numdam | MR | Zbl

[10] Mats Andersson; Elizabeth Wulcan Decomposition of residue currents, J. Reine Angew. Math., Volume 638 (2010), pp. 103-118 | MR | Zbl

[11] Mats Andersson; Elizabeth Wulcan Direct images of semi-meromorphic currents, Ann. Inst. Fourier, Volume 68 (2018) no. 2, pp. 875-900 | DOI | Numdam | MR | Zbl

[12] Daniel Barlet Le faisceau ω X · sur un espace analytique X de dimension pure, Fonctions de plusieurs variables complexes, III (Sém. François Norguet, 1975–1977) (Lecture Notes in Mathematics), Volume 670, Springer, 1978, pp. 187-204 | DOI | MR | Zbl

[13] Jan-Erik Björk Analytic 𝒟-modules and applications, Mathematics and its Applications, 247, Kluwer Academic Publishers Group, Dordrecht, 1993, xiv+581 pages | MR | Zbl

[14] Jan-Erik Björk Residues and 𝒟-modules, The legacy of Niels Henrik Abel, Springer, 2004, pp. 605-651 | DOI | Zbl

[15] Nicolas R. Coleff; Miguel E. Herrera Les courants résiduels associés à une forme méromorphe, Lecture Notes in Mathematics, 633, Springer, 1978, x+211 pages | Zbl

[16] Jean-Pierre Demailly; Mikael Passare Courants résiduels et classe fondamentale, Bull. Sci. Math., Volume 119 (1995) no. 1, pp. 85-94 | Zbl

[17] Carmen Dickenstein Canonical representatives in moderate cohomology, Invent. Math., Volume 80 (1985) no. 3, pp. 417-434 | DOI | MR | Zbl

[18] Carmen Dickenstein Résidus de formes méromorphes et cohomologie modérée, Géométrie complexe (Paris, 1992) (Actualités Sci. Indust.), Volume 1438, Hermann, 1996, pp. 35-59 | Zbl

[19] Miguel E. Herrera; David Lieberman Residues and principal values on complex spaces, Math. Ann., Volume 194 (1971), pp. 259-294 | DOI | MR | Zbl

[20] Lars Hörmander The analysis of linear partial differential operators. I, Grundlehren der Mathematischen Wissenschaften, 256, Springer, 1990, xii+440 pages (Distribution theory and Fourier analysis) | MR | Zbl

[21] Richard Lärkäng; Håkan Samuelsson Kalm Various approaches to products of residue currents, J. Funct. Anal., Volume 264 (2013) no. 1, pp. 118-138 | DOI | MR | Zbl

[22] Richard Lärkäng; Elizabeth Wulcan Residue currents and fundamental cycles, Indiana Univ. Math. J., Volume 67 (2018) no. 3, pp. 1085-1114 | DOI | MR | Zbl

[23] Jean Ruppenthal; Håkan Samuelsson Kalm; Elizabeth Wulcan Explicit Serre duality on complex spaces, Adv. Math., Volume 305 (2017), pp. 1320-1355 | DOI | MR | Zbl

[24] Håkan Samuelsson Kalm The ∂ ¯-equation, duality, and holomorphic forms on a reduced complex space, J. Geom. Anal., Volume 31 (2021) no. 2, pp. 1786-1820 | DOI | MR | Zbl

Cited by Sources: