Algebraic intermediate hyperbolicities

Dynamics of Special Points on Intermediate Jacobians

We prove some general density statements about the subgroup of invertible points on intermediate jacobians; namely those points in the Abel-Jacobi image of nullhomologous algebraic cycles on projective algebraic manifolds.

On p-adic intermediate Jacobians

For an algebraic variety $X$ of dimension $d$ with totally degenerate reduction over a $p$-adic field (definition recalled below) and an integer $i$ with $1\leq i\leq d$, we define a rigid analytic torus $J^i(X)$ together with an Abel-Jacobi mapping to it from the Chow group $CH^i(X)_{hom}$ of codimension $i$ algebraic cycles that are homologically equivalent to zero modulo rational equivalence. These tori are analogous to those defined by Griffiths using Hodge theory over the complex numbers. We compare and contrast the complex and $p$-adic theories. Finally, we examine a special case of a $p…

Projectors on the intermediate algebraic Jacobians

Let $X$ be a complex smooth projective variety of dimension $d$. Under some assumption on the cohomology of $X$, we construct mutually orthogonal idempotents in $CH_d(X \times X) \otimes \Q$ whose action on algebraically trivial cycles coincides with the Abel-Jacobi map. Such a construction generalizes Murre's construction of the Albanese and Picard idempotents and makes it possible to give new examples of varieties admitting a self-dual Chow-Künneth decomposition satisfying the motivic Lefschetz conjecture as well as new examples of varieties having a Kimura finite dimensional Chow motive. Fo…

广义 Kummer 簇的单值性及其中间 Jacobi 簇上的代数循环

The monodromy of generalized Kummer varieties and algebraic cycles on their intermediate Jacobians

本文计算广义 Kummer 簇由阿贝尔曲面导出等价诱导的单值子群并确认其为整个单值群，进而用于证明特定 Weil 型阿贝尔四维簇的 Hodge 猜想及 Kummer 型全纯辛流形上 Abel–Jacobi 映射的满射性。

Bracket Polynomial Expression of Discriminant-Resultants as SL2-invariant

We give a bracket polynomial expression for intermediate terms between discriminant and resultant for pair of binary forms. As an application of the bracket polynomial expression, we give an algebraic proof of the algebraic independence of intermediate terms, which was shown in the theory of dynamical systems.

正特征下的对角分解、中间雅可比簇与泛余维2闭链

Decomposition of the diagonal, intermediate Jacobians, and universal codimension-2 cycles in positive characteristic

本文将复三维簇稳定有理性的两类对角上同调分解障碍推广到正特征有理链连通三维簇，证明相关代数代表元的典范自对偶性，并指出特征>2时带7结点的非常一般四次双立体消解不存在泛余维2闭链类。