扇之于幺半群，犹如图式之于环：扇概念的推广
Fan is to monoid as scheme is to ring: a generalization of the notion of a fan
摘要：
根据DeMeyer，Ford & Miranda [DFM93]，我们通过声明开集是它的子扇来定义扇上的拓扑。然后，像Kato [Kat94]一样，我们通过将一束幺半群与每个扇相关联，将我们的扇变成幺半群空间。(Our（与Kato的不同）观察到这个新的monoided空间是局部同构的一些monoid的谱以同样的方式一个计划是局部同构的一些环的谱，我们定义任何monoided空间是局部同构的monoid的谱是一个（广义）风扇。幺半群代数函子然后可以用来关联一个方案到这样的风扇。如果我们在某个基域k上使用么半群代数函子，则所得到的概型是正规簇当且仅当它是复曲面簇。
英文摘要：
Following DeMeyer, Ford & Miranda [DFM93], we define a topology on a fan by declaring open sets to be its subfans. Then, like Kato [Kat94], we make our fans into monoided spaces by associating a sheaf of monoids to each fan. (Our sheaf of monoids differs from Kato's.) Observing that this new monoided space is locally isomorphic to the spectrum of some monoid in the same sort of way a scheme is locally isomorphic to the spectrum of some ring, we define any monoided space that is locally isomorphic to the spectra of monoids to be a (generalized) fan. The monoid algebra functor can then be used to associate a scheme to such a fan. If we use the monoid algebra functor over some base field k, the resultant scheme is a normal variety if and only if it is a toric variety.
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。
