小平消没定理是复几何及代数几何中的重要结果，在复流形的分类问题(例如Enriques-Kodaira Classification)上扮演重要角色。

小平邦彦起初使用流形上的霍奇理论证明，当q>0

以上M 为任何紧致凯勒流形，是M上的正规线丛，是正线丛。这个命题之后被推广为小平 中野消没定理：

当。代表在L上的所有全纯 (p,0)-形式组成的层。

In mathematics, the Kodaira vanishing theorem is a basic result of complex manifold theory and complex algebraic geometry, describing general conditions under which sheaf cohomology groups with indices q > 0 are automatically zero. The implications for the group with index q = 0 is usually that its dimension — the number of independent global sections — coincides with a holomorphic Euler characteristic that can be computed using the Hirzebruch-Riemann-Roch theorem.