论文标题
LCK歧管的代数锥具有潜力
Algebraic cones of LCK manifolds with potential
论文作者
论文摘要
如果可以将其视为HOPF歧管的复杂子手机，则复杂的歧管$ x $称为“具有潜在的LCK歧管”。令$ y $它的$ \ z $ - 覆盖，被认为是$ c^n \ backslash 0 $的复杂子手机。我们证明$ y $是代数。我们称之为以这种方式获得的歧管为代数锥，并表明$ y $上的仿射代数结构独立于$ x $的选择。我们给出了代数锥的几个内在定义，并证明这些定义是等效的。
A complex manifold $X$ is called "LCK manifolds with potential" if it can be realized as a complex submanifold of a Hopf manifold. Let $Y$ its $\Z$-covering, considered as a complex submanifold in $C^n \backslash 0$. We prove that $Y$ is algebraic. We call the manifolds obtained this way the algebraic cones, and show that the affine algebraic structure on $Y$ is independent from the choice of $X$. We give several intrinsic definitions of an algebraic cone, and prove that these definitions are equivalent.
