论文标题
曲线纤维纤维家族的Hodge-Arakelov不平等现象
Hodge-Arakelov inequalities for family of surfaces fibered by curves
论文作者
论文摘要
在平滑的准标准上，霍奇结构变化的hodge数值不变性 - 标准变体是量度混合霍奇结构的整体扭曲的复杂性。这些不变的人出现在他们可能具有更正术语的不平等现象中，称为Arakelov不平等。可以调查校正项，以使它们陷入平等，也称为Arakelov的平等性。我们研究了数值Arakelov类型（IN）的股票，用于曲线纤维的表面家族。我们的方法在重量1中使用Arakelov的身份，并在重量的2变化中使用霍奇结构（参见\ cite {ggk}），在交换性的三角形三角形中。我们建议将两个家庭的霍奇束的程度联系起来。我们还比较了在这些纤维中霍奇束的富士田分解。我们检查了霍奇数字和霍奇束的程度之间的各种身份和关系。
The Hodge numerical invariants of a variation of Hodge structure over a smooth quas--projective variety are a measure of complexity for the global twisting of the limit mixed Hodge structure when it degenerates. These invariants appear in inequalities which they may have correction terms, called Arakelov inequalities. One may investigate the correction term to make them into equalities, also called Arakelov equalities. We investigate numerical Arakelov type (in)equilities for a family of surfaces fibered by curves. Our method uses Arakelov identities in a weight 1 and also in a weight 2 variations of Hodge structure (cf. \cite{GGK}), in a commutative triangle of fibrations. We have proposed to relate the degrees of the Hodge bundles in the two families. We also compare the Fujita decomposition of Hodge bundles in these fibrations. We examine various identities and relations between Hodge numbers and degrees of the Hodge bundles in different levels.
