Decomposition, purity and fibrations by normal crossing divisors

Fouad El Zein (1) , Dung Trang Lê (2) , Xuanming Ye

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 I2M - Institut de Mathématiques de Marseille

We give a simple geometric proof of the decomposition theorem in terms of Thom-Whitney stratifications by reduction to fibrations by normal crossings divisors over the strata and explain the relation with the local purity theorem an unpublished result of Deligne and Gabber.

Domaines: Géométrie algébrique [math.AG]

Fouad El Zein, Dung Trang Lê, Xuanming Ye. Decomposition, purity and fibrations by normal crossing divisors. 2019. ⟨hal-01915674v2⟩