Develops stacky and logarithmic structures for transversely affine foliations, with the quotient stack governing linear aspects and the Kato-Nakayama space governing logarithmic-topological dynamics.
The logarithmic leaf complex and foliated d-semistability
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abstract
We study holomorphic foliations on normal crossings varieties arising as semistable degenerations. We do so by we exploring the notion of foliated d-semistability using the language of logarithmic structures in the sense of Fontaine-Illusie. First, we identify both local and global obstructions to d-semistability. In order to analyze the existence of smoothings, we develop a logarithmic deformation theory of foliations and show that the corresponding moduli functor admits a versal hull.
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math.AG 1years
2026 1verdicts
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Stacky geometry and logarithmic topology of transversely affine foliations
Develops stacky and logarithmic structures for transversely affine foliations, with the quotient stack governing linear aspects and the Kato-Nakayama space governing logarithmic-topological dynamics.