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RESEARCH PRODUCT
On GIT quotients of Hilbert and Chow schemes of curves
Margarida MeloGilberto BiniFilippo Vivianisubject
Pure mathematics14L30General MathematicsCompactified universal JacobianHilbert scheme01 natural sciencesMathematics - Algebraic GeometryMathematics::Algebraic Geometry0103 physical sciencesFOS: MathematicsProjective spaceCompactification (mathematics)0101 mathematicsAlgebraic Geometry (math.AG)QuotientMathematicsDegree (graph theory)010102 general mathematicsChow schemeGIT quotientGITModuli spaceStable curvesHilbert schemeScheme (mathematics)Settore MAT/03 - Geometria010307 mathematical physicsPseudo-stable curvedescription
The aim of this note is to announce some results on the GIT problem for the Hilbert and Chow scheme of curves of degree d and genus g in P^{d-g}, whose full details will appear in a subsequent paper. In particular, we extend the previous results of L. Caporaso up to d>4(2g-2) and we observe that this is sharp. In the range 2(2g-2)<d<7/2(2g-2), we get a complete new description of the GIT quotient. As a corollary, we get a new compactification of the universal Jacobian over the moduli space of pseudo-stable curves.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-09-16 | Electronic Research Announcements in Mathematical Sciences |