发表机构
University of Washington（华盛顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明严格高阶Du Bois奇点在小形变下不变，针对严格高阶Du Bois纤维的相对Du Bois复形建立基变换定理，展示1-Du Bois纤维的相关失效并推广局部自由性定理、证明Hodge数不变性。
AI 中文摘要
我们证明严格高阶Du Bois奇点在小形变下具有不变性。利用该性质，我们针对具有严格高阶Du Bois纤维的相对Du Bois复形证明了一个基变换定理，回答了Kovács–Taji提出的问题。我们展示了1-Du Bois纤维在形变不变性和基变换上的失效，表明严格性条件本质上是最优的。作为基变换的应用，我们将Friedman–Laza的局部自由性定理推广到光滑曲线上族的局部完全交情形之外，并证明了任意基上族的Hodge数的不变性。
英文摘要
We prove that strict higher Du Bois singularities are invariant under small deformations. Using this, we prove a base change theorem for the relative Du Bois complex with strict higher Du Bois fibers, answering a question of Kovács--Taji. We exhibit failures of deformation invariance and base change for $1$-Du Bois fibers, showing that the strictness condition is essentially sharp. We also generalize the local-freeness theorem of Friedman--Laza beyond the local complete intersection setting for families over an arbitrary base, and show the unobstructedness of deformations of strict-$1$-Du Bois canonical Calabi-Yau varieties.
Commentsv2: strengthened local freeness Theorem 1.7 over arbitrary bases and added Corollary 1.8; expanded Section 6; 38 pages
