BOCHNER-MARTINELLI FORMULAS ON SINGULAR COMPLEX SPACES

作者：Ancona Vincenzo^*; Gaveau Bernard

来源：International Journal of Mathematics, 2010, 21(2): 225-253.

DOI：10.1142/S0129167X10005994

• Bochner-Martinelli forms and kernels
• singular complex spaces
• integral formulas
• mixed Hodge structures

Let U be a complex space of complex dimension n >= 2, P a point of U, pi : (U) over tilde -> U a modification such that (U) over tilde is nonsingular and D = pi(-1)(P) is a divisor with normal crossings. A Bochner-Martinelli form on U\{P} is a partial derivative-closed differential form omega on (U) over tilde \D, of pure type (n, n - 1), logarithmic along D. Such form detects a cohomology class of H(2n-1)(U\{P}, C) on the singular space U\{P}. Thanks to a general residue formula we prove that the forms. give rise to an integral formula of Bochner-Martinelli type for holomorphic functions.
If U satisfies the following assumption that there exists a compact complex space X bimeromorphic to a Kahler manifold, and a closed subspace T subset of X, such that X\T = U (an a. ne, or a quasi-projective variety satisfies the above property), we relate Bochner-Martinelli forms to the mixed Hodge structure carried by H(2n-1)(U\{P}, C). Most of our results hold for complex spaces which are not Stein.

• 出版日期2010-2