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Semi-positivity of fiberwise Ricci-flat metrics on Calabi-Yau fibrations | | Young-Jun Choi
; | | Date: |
3 Aug 2015 | | Abstract: | Let $X$ be a K"ahler manifold which is fibered over a complex manifold $Y$
such that every fiber is a Calabi-Yau manifold. Let $omega$ be a fixed
K"ahler form on $X$. By the theorem due to Yau, there exists a unique
Ricci-flat K"ahler form $
hovert_{X_y}$ for each fiber, which is
cohomologous to $omegavert_{X_y}$. This family of Ricci-flat K"ahler forms
$
hovert_{X_y}$ induce a smooth $(1,1)$-form $
ho$ on $X$. In this paper, we
prove that $
ho$ is semi-positive on the total space $X$. We also discuss
several byproducts, among them the local triviality of families of Calabi-Yau
manifolds. | | Source: | arXiv, 1508.0323 | | Services: | Forum | Review | PDF | Favorites | |
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