向量包在奥尔森粉丝上的研究
Vector bundles on Olsson fans
AI总结：
本文研究了弱凸奥尔森粉丝的几何性质，探讨了其上向量包的模栈结构及Weyl凸性在其中的表现。
摘要：
Artin粉丝是锥复形的代数几何体现。我们研究弱凸奥尔森粉丝，通过两种方式推广Artin粉丝：首先，它们允许直线性空间，因此包括热带环面；其次，它们定义在基础对数方案上，因此提供了一个相对的等变托里几何版本。我们确定了奥尔森粉丝在何种条件下是良好的，即其几何由组合方式决定。我们研究了奥尔森粉丝上的拟 coherent sheaves，特别是向量包：我们描述了在锥（细分）情况下的模栈，并在一般情况下讨论了一些代数性失败；Weyl凸性在此背景下自然出现。
英文摘要：
Artin fans are algebro-geometric incarnations of cone complexes. We study weakly convex Olsson fans, generalising Artin fans in two ways: first, they admit lineality spaces, thus including tropical tori as well; second, they are defined over a base logarithmic scheme, thus providing a relative version of equivariant toric geometries. We determine conditions under which Olsson fans are well-behaved, in the sense that their geometry is determined combinatorially. We undertake the study of quasicoherent sheaves, and in particular vector bundles, on Olsson fans: we describe their moduli stack in the case of a (subdivided) cone, and some failures of algebraicity in the general case; Weyl convexity shows up naturally in this context.
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