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Resumen:
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Let T and V be complex analytic spaces, with T reduced and locally irreducible and ?:T×V?T the projection map to the first factor. Let K ? be a complex 0?K n ? X n K n?1 ? X n?1 …? X 2 K 1 ? X 1 K 0 ?0 of O T×V coherent sheaves, where all X j are O T×V -linear, all sheaves K j are O T -flat and such that the support of the homology sheaves H j (K ? ) is ? -finite. For every t?T , V t denotes {t}×V?V ; K ? t denotes the complex obtained by tensoring K ? with O V t ; K ? t;p denotes the complex formed by the germs at (t,p) of K ? t and H j (K ? t;p ) denotes the j th homology group of the complex K ? t;p . The Euler characteristic of the complex of sheaves K ? t at a point (t,p)?V t is defined as ?(K ? t;p )=? j=0 n (?1) j dim C H j (K ? t;p ). The authors show that, for every (t 0 ,p 0 )?T×V there are neighbourhoods T ? and V ? of t 0 and p 0 , respectively, such that for every t?T ? , ?(K ? t 0 ;p 0 )=? q?V ? ?(K ? t;p ) .
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