论文标题
阳性特征中品种的霍奇环
The Hodge ring of varieties in positive characteristic
论文作者
论文摘要
让$ k $成为一个积极特征的领域。我们证明，hodge数字$ h^{i，j}（x）= \ dim h^j（x，ω_x^i）$之间的唯一线性关系是每个光滑的$ x $ of $ k $的$ x $ a $ y $ k $。 We also show that the only linear combinations of Hodge numbers that are birational invariants of $X$ are given by the span of the $h^{i,0}(X)$ and the $h^{0,j}(X)$ (and their duals $h^{i,n}(X)$ and $h^{n,j}(X)$). Kähler歧管的相应陈述由Kotschick和Schreieder证明。
Let $k$ be a field of positive characteristic. We prove that the only linear relations between the Hodge numbers $h^{i,j}(X) = \dim H^j(X,Ω_X^i)$ that hold for every smooth proper variety $X$ over $k$ are the ones given by Serre duality. We also show that the only linear combinations of Hodge numbers that are birational invariants of $X$ are given by the span of the $h^{i,0}(X)$ and the $h^{0,j}(X)$ (and their duals $h^{i,n}(X)$ and $h^{n,j}(X)$). The corresponding statements for compact Kähler manifolds were proven by Kotschick and Schreieder.
