Geodesic
The Dolbeault complex in infinite dimensions I
Lempert, László1
1 Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Journal of the American Mathematical Society, Tome 11 (1998) no. 3, pp. 485-520

Voir la notice de l'article provenant de la source American Mathematical Society

In this paper we introduce certain basic notions concerning infinite dimensional complex manifolds, and prove that the Dolbeault cohomology groups of infinite dimensional projective spaces, with values in finite rank vector bundles, vanish. Some applications of such vanishing theorems are discussed; e.g., we classify vector bundles of finite rank over infinite dimensional projective spaces. Finally, we prove a sharp theorem on solving the inhomogeneous Cauchy–Riemann equations on affine spaces.
DOI : 10.1090/S0894-0347-98-00266-5

Lempert, László 1

1 Department of Mathematics, Purdue University, West Lafayette, Indiana 47907 
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Lempert, László. The Dolbeault complex in infinite dimensions I. Journal of the American Mathematical Society, Tome 11 (1998) no. 3, pp. 485-520. doi: 10.1090/S0894-0347-98-00266-5

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