On moduli of foliated surfaces
Calum Spicer, Roberto Svaldi, Sebastian Velazquez
TL;DR
This paper introduces a framework for classifying foliated surfaces using moduli spaces, establishing that the moduli functor is representable by a Deligne-Mumford stack, thus advancing the understanding of foliated surface families.
Contribution
It defines stable families of foliations and proves the moduli functor for foliated surfaces is representable by a Deligne-Mumford stack, providing a new structure for their classification.
Findings
Defined stable families of foliations.
Proved the moduli functor is representable by a Deligne-Mumford stack.
Established foundational results for the moduli of foliated surfaces.
Abstract
We present a definition of stable family of foliations and show that the corresponding moduli functor for foliated surfaces is representable by a Deligne-Mumford stack.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology