光滑填充問題之探究

Abstract

我們研究射影退化中的「光滑填充」問題，即：當一個代數多樣體具有光滑的一般纖維時，是否能將其替換為具有相同一般纖維的光滑家族。在本文中，我們構造了一個三次三維體退變的反例——此退化的單值群有限，但無法被光滑的射影家族所填充。

We study the ”smooth filling‐in” problem for projective degenerations—when a one-parameter family with smooth general fibers can be replaced by a smooth family which has the same general fibers. In this article, we construct a counterexample—a degeneration of cubic threefolds with single A2 singularity—which has monodromy of finite order but cannot be filled with a smooth projective family.