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Article Dans Une Revue Annales de l'Institut Fourier Année : 2015

On the torsion of the first direct image of a locally free sheaf

Andrei Teleman

Résumé

Let $\pi:M\to B$ be a proper holomorphic submersion between complex manifolds and ${\cal E}$ a holomorphic bundle on $M$. We study and describe explicitly the torsion subsheaf $\mathrm{Tors}(R^1\pi_*({\cal E}))$ of the first direct image $R^1\pi_*({\cal E})$ under the assumption $R^0\pi_*({\cal E})=0$. We give two applications of our results. The first concerns the locus of points in the base of a generically versal family of complex surfaces where the family is non-versal. The second application is a vanishing result for $H^0(\mathrm{Tors}(R^1\pi_*({\cal E})))$ in a concrete situation related to our program to prove existence of curves on class VII surfaces.

Dates et versions

hal-01221911 , version 1 (28-10-2015)

Identifiants

Citer

Andrei Teleman. On the torsion of the first direct image of a locally free sheaf. Annales de l'Institut Fourier, 2015, 65 (1), pp.101-136. ⟨10.5802/aif.2926⟩. ⟨hal-01221911⟩
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