对数可微空间与带角流形
Log differentiable spaces and manifolds with corners
摘要：
我们开发了一个一般的理论的日志空间，其中可以使意义上的基本概念的对数几何，在意义上的Fontaine-Illusie-加藤。我们用对数空间所作的许多一般构造是新的，甚至在代数的情况下也是如此。在可微的设置，我们的理论产生了一个框架来处理流形的角落推广最近的工作Kottke-Melrose。我们给一个治疗的理论球迷，这是monoid计划是环。通过采用类似的结果，从对数代数几何，我们证明了一个一般的结果，解决复曲面奇点，可用于解决一类广泛的“日志光滑”空间的奇点。
英文摘要：
We develop a general theory of log spaces, in which one can make sense of the basic notions of logarithmic geometry, in the sense of Fontaine-Illusie-Kato. Many of our general constructions with log spaces are new, even in the algebraic setting. In the differentiable setting, our theory yields a framework for treating manifolds with corners generalizing recent work of Kottke-Melrose. We give a treatment of the theory of fans, which are to monoids as schemes are to rings. By adapting similar results from logarithmic algebraic geometry, we prove a general result on resolution of toric singularities which can be used to resolve singularities of a wide class of "log smooth" spaces.
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。
