Moduli Spaces of Stable Polygons and Symplectic Structures on $\bar{M}_{0,n}$

dc.creatorHu, Yi
dc.date1997-01-27
dc.date1998-08-28
dc.date.accessioned2026-07-07T09:02:52Z
dc.date.available2026-07-07T09:02:52Z
dc.descriptionIn this paper, certain natural and elementary polygonal objects in Euclidean space, {\it the stable polygons}, are introduced, and the novel moduli spaces ${\bfmit M}_{{\bf r}, ε}$ of stable polygons are constructed as complex analytic spaces. Quite unexpectedly, these new moduli spaces are shown to be projective and isomorphic to the moduli space $\bar{\cM}_{0,n}$ of the Deligne-Mumford stable curves of genus 0. Further, built into the structures of stable polygons are some natural data leading toward to a family of (classes of) symplectic (Kähler) forms. To some degree, ${\bfmit M}_{{\bf r}, ε}$ may be considered as symplectic counterparts of $\bar{\cM}_{0,n}$ and Kapranov's Chow quotient construction of $\bar{\cM}_{0,n}$. All these together brings up a new tool to study the Kähler topology of $\bar{\cM}_{0,n}$.
dc.descriptionEnlarged version, 7 figures added. 35 pages. To appear in Compositio Mathematica
dc.identifierhttps://arxiv.org/abs/dg-ga/9701011
dc.identifierhttp://arxiv.org/abs/dg-ga/9701011
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/148788
dc.subjectDifferential Geometry
dc.subjectAlgebraic Geometry
dc.titleModuli Spaces of Stable Polygons and Symplectic Structures on $\bar{M}_{0,n}$
dc.typetext

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