Complex multiplication, Griffiths-Yukawa couplings, and rigidity for families of hypersurfaces

On the Griffiths-Yukawa coupling length of some Calabi-Yau families

We determine the Griffiths-Yukawa coupling length of the Calabi-Yau universal families coming from hyperplane arrangements.

Fubini-Griffiths-Harris rigidity of homogeneous varieties

Upper bounds on projective rigidity of each homogeneously embedded homogeneous variety are determined; and a new, invariant characterization of the Fubini forms is given.

Griffiths-Harris rigidity of compact Hermitian symmetric spaces

I show that any complex manifold that resembles a rank two compact Hermitian symmetric space (other than a quadric hypersurface) to order two at a general point must be an open subset of such a space.

Fubini-Griffiths-Harris rigidity and Lie algebra cohomology

We prove a general extrinsic rigidity theorem for homogeneous varieties in $\mathbb{CP}^N$. The theorem is used to show that the adjoint variety of a complex simple Lie algebra $\mathfrak{g}$ (the unique minimal G orbit in $\mathbb{P}\mathfrak{g}$) is extrinsically rigid to third order. In contrast, we show that the adjoint variety of $SL_3\mathbb{C}$, and the Segre product $\mathit{Seg}(\mathbb{P}^1\times \mathbb{P}^n)$, both varieties with osculating sequences of length two, are flexible at order two. In the $SL_3\mathbb{C}$ example we discuss the relationship between the extrinsic projectiv…

$A_2$、$B_2$、$G_2$ 型 Hitchin 系统的 Donagi-Markman 三次型

Donagi-Markman cubics for Hitchin systems of type A2, B2. G2

本文通过计算 Balduzzi-Pantev 公式中的二次留数，获得了 $A_2$、$B_2$ 和 $G_2$ 型 Hitchin 系统的 Donagi-Markman 三次型显式公式，并恢复了 $G_2$ 的早先结果。