论文标题
从形式平滑到几何平滑
From formal smoothings to geometric smoothings
论文作者
论文摘要
令X为代数封闭的场上的投影，等二维的单数方案。然后，存在几何平滑的存在（即X在平滑的基本曲线上的变形家族，其通用纤维是光滑的）意味着存在Tziolas定义的形式平滑。在本文中，我们解决了相反的问题，给出了X上足够的条件，以保证相反的问题，即形式的平稳性意味着几何平稳性。鉴于Tziolas的结果给出了足够的标准，这对形式平滑的存在很有用。
Let X be a projective, equidimensional, singular scheme over an algebraically closed field. Then the existence of a geometric smoothing (i.e. a family of deformations of X over a smooth base curve whose generic fibre is smooth) implies the existence of a formal smoothing as defined by Tziolas. In this paper we address the reverse question giving sufficient conditions on X that guarantee the converse, i.e. formal smoothability implies geometric smoothability. This is useful in light of Tziolas' results giving sufficient criteria for the existence of formal smoothings.
