On the direct image of the adjoint line bundle

Indranil Biswas, Fatima Laytimi, D. S. Nagaraj +1

We give an algebraic-geometric proof of the fact that for a smooth fibration $\pi :X⟶Y$ of projective varieties, the direct image ${\pi }_{\ast }(L\otimes K_{X/Y})$ of the adjoi…