Stability of Tails and 4-Canonical Models

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dc.creatorHyeon, Donghoon
dc.creatorMorrison, Ian
dc.date2008-06-09
dc.date2009-03-09
dc.date.accessioned2026-07-07T12:49:43Z
dc.date.available2026-07-07T12:49:43Z
dc.descriptionWe show that the GIT quotients of suitable loci in the Hilbert and Chow schemes of 4-canonically embedded curves of genus $g\ge 3$ are the moduli space $\bar{M}_g^{\text{ps}}$ of pseudo-stable curves constructed by Schubert in \cite{Schubert} using Chow varieties and 3-canonical models. The only new ingredient needed in the Hilbert scheme variant is a more careful analysis of the stability with respect to a certain 1-ps $λ$ of the $m^{\text{th}}$ Hilbert points of curves $X$ with elliptic tails. We compute the exact weight with which $λ$ acts, and not just the leading term in $m$ of this weight. A similar analysis of stability of curves with rational cuspidal tails allows us to determine the stable and semistable 4-canonical Chow loci. Although here the geometry of the quotient is more complicated because there are strictly semi-stable orbits, we are able to again identify it as $\bar{M}_g^{\text{ps}}$. Our computations yield, as byproducts, examples of both $m$-Hilbert unstable and $m$-Hilbert stable $X$ that are Chow strictly semi-stable.
dc.identifierhttps://arxiv.org/abs/0806.1269
dc.identifierhttp://arxiv.org/abs/0806.1269
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222469
dc.subjectAlgebraic Geometry
dc.subject14L24; 14H10
dc.titleStability of Tails and 4-Canonical Models
dc.typetext

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