The authors develop a logarithmic deformation theory for foliations on normal crossings varieties arising as semistable degenerations and prove that the corresponding moduli functor admits a versal hull.
arXiv preprint arXiv:1006.5870 , year=
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abstract
We discuss the role played by logarithmic structures in the theory of moduli.
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The integral Chow ring of M_0(P^r, 2) is presented as a quotient of a three-variable polynomial ring with all non-trivial relations encoded by two rational generating functions.
The paper proves continuity of deformed mass and phase functions on stability condition spaces, deduces a homeomorphic embedding into measures, and establishes a triangle inequality plus truncation estimates.
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The logarithmic leaf complex and foliated d-semistability
The authors develop a logarithmic deformation theory for foliations on normal crossings varieties arising as semistable degenerations and prove that the corresponding moduli functor admits a versal hull.
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The integral Chow ring of M_0(P^r, 2) is presented as a quotient of a three-variable polynomial ring with all non-trivial relations encoded by two rational generating functions.
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Properties of deformed mass and phase functions
The paper proves continuity of deformed mass and phase functions on stability condition spaces, deduces a homeomorphic embedding into measures, and establishes a triangle inequality plus truncation estimates.