发表机构
Chongqing University of Technology（重庆理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在不假设单连通性的条件下，通过构造自由商和Igusa商例子，回答了Huybrechts关于Calabi-Yau三维流形切丛刚性与奇异形变空间的两个问题，并给出了三维反例及形变芽的显式结构。
AI 中文摘要
我们研究了Huybrechts关于Calabi-Yau三维流形上切丛的刚性与奇异形变空间的两个问题，且不假设单连通性。我们的第一个例子是$\mathbb P^7$中四个二次曲面光滑交点的自由$(\mathbb Z/2)^3$商。其切丛是稳定的且无穷小刚性的，同时也为Peternell问题1.6中提出的分类提供了一个三维反例。对于三条椭圆曲线乘积的经典Igusa商，我们在保持底层三维流形固定的情况下，确定了其半直和切丛的解析半万有形变芽。该芽同构于$\mathbb C^3$中三条坐标轴并集的两份拷贝的乘积。因此它是约化且奇异的，具有九个二维不可约分支。
英文摘要
We address two questions of Huybrechts concerning rigidity and singular deformation spaces of tangent bundles on Calabi--Yau threefolds, without assuming simple connectedness. Our first example is a free $(\mathbb Z/2)^3$ quotient of a smooth intersection of four quadrics in $\mathbb P^7$. Its tangent bundle is stable and infinitesimally rigid, and it also provides a three-dimensional counterexample to the proposed classification in Peternell's Question~1.6. For a classical Igusa quotient of a product of three elliptic curves, we determine the analytic semiuniversal deformation germ of its polystable tangent bundle, keeping the underlying threefold fixed. This germ is isomorphic to the product of two copies of the union of the three coordinate axes in $\mathbb C^3$. It is therefore reduced and singular, with nine two-dimensional irreducible components.
