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Abstract:

Let D: Ω → Ω be a differential operator defined in the exterior algebra Ω of differential forms over the polynomial ring S in n variables. In this work we give conditions for deforming the module structure of Ω over S induced by the differential operator D, in order to make D an S-linear morphism while leaving the C-vector space structure of Ω unchanged. One can then apply the usual algebraic tools to study differential operators: finding generators of the kernel and image, computing a Hilbert polynomial of these modules, etc. Taking differential operators arising from a distinguished family of derivations, we are able to classify which of them allow such deformations on Ω. Finally we give examples of differential operators and the deformations that they induce. © 2016, The Managing Editors.

Registro:

Documento: Artículo
Título:Deformations of the exterior algebra of differential forms
Autor:Molinuevo, A.
Filiación:Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires, CP C1428EGA, Argentina
Palabras clave:Differential operators; Exterior algebra; Modules; Order one
Año:2016
Volumen:57
Número:4
Página de inicio:771
Página de fin:787
DOI: http://dx.doi.org/10.1007/s13366-016-0299-1
Título revista:Beitrage zur Algebra und Geometrie
Título revista abreviado:Beitr. Algebr. Geom.
ISSN:01384821
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01384821_v57_n4_p771_Molinuevo

Referencias:

  • Camacho, C., Lins Neto, A., The topology of integrable differential forms near a singularity (1982) Inst. Hautes Études Sci. Publ. Math. (55), pp. 5-35. , http://www.numdam.org/item?id=PMIHES_1982__55__5_0
  • Cukierman, F., Pereira, J.V., Vainsencher, I., Stability of foliations induced by rational maps (2009) Ann. Fac. Sci. Toulouse Math. (6), 18 (4), pp. 685-715. , http://afst.cedram.org/item?id=AFST_2009_6_18_4_685_0
  • Grothendieck, A., Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. IV (1967) Inst. Hautes Études Sci. Publ. Math. (32), p. 361
  • Herrera, M., Lieberman, D., Duality and the de Rham cohomology of infinitesimal neighborhoods (1971) Invent. Math., 13, pp. 97-124
  • Jouanolou, J.P., (1979) Équations de Pfaff algébriques. Lecture Notes in Mathematics, , 708, Springer, Berlin
  • Michor, P.W., (2008) Topics in Differential Geometry, Graduate Studies in Mathematics, , 93, American Mathematical Society, Providence
  • Molinuevo, A., Unfoldings and deformations of rational and logarithmic foliations (2016) Ann. Inst. Fourier (Grenoble), 66 (4), pp. 1583-1613
  • Warner, F.W.: Foundations of Differentiable Manifolds and Lie Groups, Graduate Texts in Mathematics, vol. 94. Springer, New York (1983) (Corrected reprint of the 1971 edition)

Citas:

---------- APA ----------
(2016) . Deformations of the exterior algebra of differential forms. Beitrage zur Algebra und Geometrie, 57(4), 771-787.
http://dx.doi.org/10.1007/s13366-016-0299-1
---------- CHICAGO ----------
Molinuevo, A. "Deformations of the exterior algebra of differential forms" . Beitrage zur Algebra und Geometrie 57, no. 4 (2016) : 771-787.
http://dx.doi.org/10.1007/s13366-016-0299-1
---------- MLA ----------
Molinuevo, A. "Deformations of the exterior algebra of differential forms" . Beitrage zur Algebra und Geometrie, vol. 57, no. 4, 2016, pp. 771-787.
http://dx.doi.org/10.1007/s13366-016-0299-1
---------- VANCOUVER ----------
Molinuevo, A. Deformations of the exterior algebra of differential forms. Beitr. Algebr. Geom. 2016;57(4):771-787.
http://dx.doi.org/10.1007/s13366-016-0299-1