Artículo
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
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- 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
