Seminar on Geometric Complex Analysis

Date, time & place	Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.)
Organizer(s)	Kengo Hirachi, Shigeharu Takayama

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yongpan Zou (Univ. of Tokyo)
Positivity of twisted direct image sheaves (English)

[ Abstract ]
For a projective surjective morphism

$f: X \to Y$ of complex manifolds with connected fibers, let

$L$ be a line bundle on

$X$ . We are interested in the direct image

$f_*(K_{X/Y} \otimes L)$ . In general, the positivity of the bundle

$L$ induces positivity in the direct image sheaves. Specifically, when

$L$ is a big and nef line bundle, the vector bundle

$f_*(K_{X/Y} \otimes L)$ is big. This is joint work with Y. Watanabe.

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