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Degeneracy Loci of Vector Bundle Maps and Ampleness

2002
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Mathematica Scandinavica
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jørgen anders geertsen don't vanish at all, namely those of the form (λ, σ ) where λ ∈ k \ {0}, and the other sections vanish too much, namely on a line, i.e. in codimension 1. So even for very nice globally generated bundles it can happen that no X k (φ) has the 'right' dimension. We define the number t k = t k (X, E, F ) as follows: Note that since we can take for φ the zero-morphism 0 : E → F , which has X k (0) = X for all k, the number t k is well-defined and t k ≤ dim X. Also, the

doi:10.7146/math.scand.a-14359
fatcat:2kkhylhhg5dwdd6gmgot47mrke