ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 30, 31, 32 Ben Messaoud, Hèdi, Université de Monastir, Tunisia New slicing formula Let X be a complex analytic subset of Δ^{n} the unit polydisk in ℂ^{n}, of pure dimension p and let υ be a psh and bounded function in Δ^{p}. We extend Federer’s slicing formula: ∫_{X} φ(dd^{c}υ)^{p} = ∫_{a∈Δ^{p}}[X_{a}](φ)(dd^{c}υ)^{p}(a) where φ ∈ D(Δ^{n}), [X_{a}](φ) is the average of φ over the slice X_{a} := X ∩ a × ℂ^{n−p} and (dd^{c}υ)^{p} is the Monge-Ampère measure. Here the exceptional set is pluripolar. Applications to the extension of positive d-closed current over pluripolar sets with condition on slices will be presented. These results are joint work with H. Elmir. Reference: H. Ben Messaoud, and H. Elmir, Tranchage et prolongement des courants positifs fermés, Math. Ann. 307 473 - 487 (1997).