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- W4313483472 abstract "We consider the curvature strict positivity of the direct image bundle associated to a pseudoconvex family of bounded domains. The main result is that the curvature of the direct image bundle associated to a strictly pseudoconvex family of bounded circular domains or Reinhardut domains are strictly positive in the sense of Nakano, even if the weight functions are not strictly plurisubharmonic. This result gives a new geometric insight about the property of strict pseudoconvexity, and has some applications in complex analysis and convex analysis. We investigate that the main result implies a remarkable result of Berndtsson which states that, for an ample vector bundle $E$ over a compact complex manifold $X$ and any $kgeq 0$, the bundle $S^kEotimesdet E$ admits a Hermitian metric whose curvature is strictly positive in the sense of Nakano, where $S^kE$ is the $k$-th symmetric product of $E$. The two main ingredients in the argument of the main theorems are Berndtsson's estimate of the lower bound of curvature of direct image bundles and Deng-Ning-Wang-Zhou's characterization of the curvature Nakano positivity of Hermitian vector bundles in terms of $L^2$-estimate of $barpartial$." @default.
- W4313483472 created "2023-01-06" @default.
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- W4313483472 date "2022-12-31" @default.
- W4313483472 modified "2023-09-30" @default.
- W4313483472 title "Curvature strict positivity of direct image bundles associated to pseudoconvex families of domains" @default.
- W4313483472 doi "https://doi.org/10.48550/arxiv.2301.00160" @default.
- W4313483472 hasPublicationYear "2022" @default.
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