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Abstract des Vortrages von Olivia Dumitrescu

Elementary (-1) cycles in P^n

We use birational geometry of P^n to describe the Cremona action on r cycles on the blown up P^n. We first describe the Cremona map as a composition of flops on the blown-up projective space at the coordinate points. Mainly the Cremona map blows up all r dimensional linear cycles and contracts the proper directions of the exceptional divisors in a precise order. In particular, we construct examples of special effect varieties in the blown up P^n that we call elementary (-1) r-cycles. For r=1 our construction of elementary (-1) curves in the blown-up P^n generalizes the standard construction of (-1) curves in the blown up P^2 as well as the construction of elementary (-1) curves in the blown up P^3. We present applications of this construction to interpolation problems in P^n. This is joint work with Rick Miranda.