沿子层的变形
Deformations along subsheaves
摘要：
令f：Y -> X是复射影流形的一个态射，设F是切丛在李括号下闭的一个子层，但不一定是一个叶理。这篇短文包含了一个基本的和非常几何的论证，证明了沿着层F变形态射f的所有障碍都位于层F_Y的第一个上同调群H ^1（Y，F_Y）中，它是包含映射拉回下f^*（F）在f^*（T_X）中的像。这一结果的特殊情况包括沿（可能是奇异的）叶理的变形理论，对数变形理论和变形与不动点。
英文摘要：
Let f : Y -> X be a morphism of complex projective manifolds, and let F be a subsheaf of the tangent bundle which is closed under the Lie bracket, but not necessarily a foliation. This short paper contains an elementary and very geometric argument to show that all obstructions to deforming the morphism f along the sheaf F lie in the first cohomology group H^1(Y, F_Y) of the sheaf F_Y, which is the image of f^*(F) in f^*(T_X) under the pull-back of the inclusion map. Special cases of this result include the theory of deformation along a (possibly singular) foliation, logarithmic deformation theory and deformations with fixed points.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
