具有孤立奇点的紧Calabi–Yau与Fano簇的形变
Deformations of Compact Calabi--Yau and Fano Varieties with Isolated Singularities
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中文总结 AI 辅助
该研究针对带孤立奇点的紧对数典范凯勒簇，推广了Tenie与Namikawa的相关结果，证明其半通用形变的一般纤维满足特定Du Bois与链环不变量条件。
中文摘要 AI 辅助
设X为紧的、具有平凡典范层且带孤立奇点的对数典范凯勒n维簇，n≥3。我们证明，X的半通用形变的一般纤维在奇点处的Du Bois不变量b^{1,n-2}=0。在X满足某一拓扑假设的条件下，一般纤维的链环不变量l^{1,n-2}=0。若X为紧的、具有丰富反典范层且带孤立奇点的射影对数典范n维簇，n≥3，则一般纤维满足b^{1,n-2}=l^{1,n-2}=0（无需拓扑假设）。这些结果推广了Tenie《奇异Fano与Calabi–Yau簇的整体光滑化》的近期成果及Namikawa《Calabi–Yau三维簇的形变理论与若干奇点不变量》的旧有结果。
英文摘要
Let $X$ be a compact log-canonical Kähler $n$-fold, $n\ge3,$ with trivial canonical sheaf and with isolated singularities. We prove that the generic fibres of a semi-universal deformation of $X$ have Du Bois invariant $b^{1,n-2}=0$ at the singular points. Under a certain topological hypothesis on $X$ the generic fibres have also link invariant $l^{1,n-2}=0.$ If $X$ is a projective log-canonical $n$-fold, $n\ge3,$ with ample anti-canonical sheaf and with isolated singularities then the generic fibres have $b^{1,n-2}=l^{1,n-2}=0$ (without the topological hypothesis). These are generalizations of recent results of Tenie `Global smoothing of singular Fano and Calabi--Yau varieties' and an older result of Namikawa `Deformation theory of Calabi--Yau threefolds and certain invariants of singularities.'
