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Generic inner projections of projective varieties and an application to the positivity of double point divisors

2014
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Transactions of the American Mathematical Society
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Let X ⊆ P N be a smooth nondegenerate projective variety of dimension n ≥ 2, codimension e and degree d with the canonical line bundle ω X defined over an algebraically closed field of characteristic zero. The purpose here is to prove that the base locus of |O X (d − n − e − 1) ⊗ ω ∨ X | is at most a finite set, except in a few cases. To describe the exceptional cases, we classify (not necessarily smooth) projective varieties whose generic inner projections have exceptional divisors. As

doi:10.1090/s0002-9947-2014-06129-1
fatcat:74zbuhkdm5b3rp2gn35w3x7d3m