Differential geometry, especially the use of curvature, plays a central role in modern Hodge theory. The vector bundles that occur in the theory (Hodge bundles) have metrics given by the polarizations of the Hodge structures, and the sign and singularity properties of the resulting curvatures have far reaching implications in the geometry of families of algebraic varieties. A special property of the curvatures is that they are 1st order invariants expressed in terms of the norms of algebro-geometric bundle mappings. This partly expository paper will explain some of the positivity and singularity properties of the curvature invariants that arise in the Hodge theory with special emphasis on the norm property.

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矢量丛的正性和霍奇理论

微分几何，尤其是曲率的使用，在现代霍奇理论中起着核心作用。理论中出现的向量丛（霍奇丛）具有由霍奇结构的极化给出的度量，并且由此产生的曲率的符号和奇点性质在代数簇的几何学中具有深远的影响。曲率的一个特殊性质是它们是1英石用代数几何束映射的范数表示的顺序不变量。这篇部分解释性的论文将解释霍奇理论中出现的曲率不变量的一些正性和奇异性性质，特别强调范数性质。