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Log differentiable spaces and manifolds with corners
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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.
Forward citations
Cited by 2 Pith papers
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The motivic fundamental groupoid at tangential basepoints
A general motivic fundamental groupoid at tangential basepoints is constructed over any field, with Betti and de Rham realizations matching the classical fundamental torsor and periods given by regularized iterated integrals.
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An introduction to real oriented blowups in toric, toroidal and logarithmic geometries
An expository review explaining that rounding of complex log spaces generalizes real oriented blowups and builds canonical representatives for links of singularities and Milnor fibers.
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