Partial intersections and graded Betti numbers.
In this paper we study some aspects of the cohomology of groups and we construct a central extension of the symplectic group .
We study 0-dimensional real rank one valuations centered in a regular local ring of dimension n > 2 such that the associated valuation ring can be obtained from the regular ring by a sequence of quadratic transforms. We define two classical invariants associated to the valuation (the refined proximity matrix and the multiplicity sequence) and we show that are equivalent data of the valuation.