On surfaces in P^6 with no trisecant lines

Mathematics – Algebraic Geometry

Scientific paper

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21 pages, DVI file available at http://www.math.kth.se/~sandra/Welcome Mittag-Leffler Report No 13, 1996/97 Latex

Scientific paper

We construct examples of smooth surfaces S in P^6 with no trisecant lines.
This list includes examples of surfaces not cut out by quadrics. We prove that
unless S has a finite number of disjoint $(-1)$-lines, and each one meets some
other line L on the surface with L^2\leq -2, and S is not an inner projection
from P^7 the surface belongs to the list of examples.

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