The Hodge structure of semiample hypersurfaces and a generalization of the monomial-divisor mirror map

周期图像的Baily-Borel紧化与b-半 ample猜想

Baily--Borel compactifications of period images and the b-semiampleness conjecture

本文研究了Hodge理论中线束的半 ample性，证明了Calabi-Yau Hodge结构的Hodge束在特定条件下是半 ample的，并推导了b-半 ample猜想。

Answer to a question by Fujita on Variation of Hodge Structures

We first provide details for the proof of Fujita's second theorem for Kähler fibre spaces over a curve, asserting that the direct image $V$ of the relative dualizing sheaf splits as the direct sum $ V = A \oplus Q$, where $A$ is ample and $Q$ is unitary flat. Our main result then answers in the negative the question posed by Fujita whether $V$ is semiample. In fact, $V$ is semiample if and only if $Q$ is associated to a representation of the fundamental group of $B$ having finite image. Our examples are based on hypergeometric integrals.

Hodge环和CM阿贝尔簇上解析周期之间的二次关系

Hodge cycles and quadratic relations between holomorphic periods on CM abelian varieties

本文研究了CM阿贝尔簇上解析周期的Hodge关系，证明通过单调二次关系可生成所有非平凡关系，并展示了构造的B在特定域上的分裂性质。

Toric residue and combinatorial degree

Consider an n-dimensional projective toric variety X defined by a convex lattice polytope P. David Cox introduced the toric residue map given by a collection of n+1 divisors Z_0,...,Z_n on X. In the case when the Z_i are T-invariant divisors whose sum is X\T the toric residue map is the multiplication by an integer number. We show that this number is the degree of a certain map from the boundary of the polytope P to the boundary of a simplex. This degree can be computed combinatorially. We also study radical monomial ideals I of the homogeneous coordinate ring of X. We give a necessary and suf…

内生于项序交换代数的Gröbner基，及其在子式Hodge代数中的应用

Gröbner Bases Native to Term-ordered Commutative Algebras, with Application to the Hodge Algebra of Minors

为深入理解双行列式基，本文为配备单项式概念与项序的交换代数发展了内生的Gröbner基理论与算法，并借此为任意t-子式理想给出了通用Gröbner基的简明证明。

From standard monomial theory to semi-toric degenerations via Newton-Okounkov bodies

The Hodge algebra structures on the homogeneous coordinate rings of Grassmann varieties provide semi-toric degenerations of these varieties. In this paper we construct these semi-toric degenerations using quasi-valuations and triangulations of Newton-Okounkov bodies.