Higher Complex Structures
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Abstract We introduce and analyze a new geometric structure on topological surfaces generalizing the complex structure. To define this so-called higher complex structure, we use the punctual Hilbert scheme of the plane. The moduli space of higher complex structures is defined and is shown to be a generalization of the classical Teichmüller space. We give arguments for the conjectural isomorphism between the moduli space of higher complex structures and Hitchin’s component.
1998 ◽
Vol 09
(01)
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pp. 1-45
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2006 ◽
Vol 08
(04)
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pp. 481-534
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2018 ◽
Vol 49
(1)
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pp. 129-149
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2000 ◽
Vol 23
(1)
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pp. 87-100
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