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024 7 $a10.1007/978-3-319-11337-1
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100   $a20141107d2014      u|         0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aGeometric Invariant Theory for Polarized Curves /$fby Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani
205   $a1st ed. 2014.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014.
215   $a1 online resource (X, 211 p. 17 illus.)
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2122
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-319-11336-4 
320   $aIncludes bibliographical references and index.
327   $aIntroduction -- Singular Curves -- Combinatorial Results -- Preliminaries on GIT -- Potential Pseudo-stability Theorem -- Stabilizer Subgroups -- Behavior at the Extremes of the Basic Inequality -- A Criterion of Stability for Tails -- Elliptic Tails and Tacnodes with a Line -- A Strati_cation of the Semistable Locus -- Semistable, Polystable and Stable Points (part I) -- Stability of Elliptic Tails -- Semistable, Polystable and Stable Points (part II) -- Geometric Properties of the GIT Quotient -- Extra Components of the GIT Quotient -- Compacti_cations of the Universal Jacobian -- Appendix: Positivity Properties of Balanced Line Bundles.  .
330   $aWe investigate GIT quotients of polarized curves. More specifically, we study the GIT problem for the Hilbert and Chow schemes of curves of degree d and genus g in a projective space of dimension d-g, as d decreases with respect to g. We prove that the first three values of d at which the GIT quotients change are given by d=a(2g-2) where a=2, 3.5, 4. We show that, for a>4, L. Caporaso's results hold true for both Hilbert and Chow semistability. If 3.5<a<4, the Hilbert semistable locus coincides with the Chow semistable locus and it maps to the moduli stack of weakly-pseudo-stable curves. If 2<a<3.5, the Hilbert and Chow semistable loci coincide and they map to the moduli stack of pseudo-stable curves. We also analyze in detail the critical values a=3.5 and a=4, where the Hilbert semistable locus is strictly smaller than the Chow semistable locus. As an application, we obtain three compactications of the universal Jacobian over the moduli space of stable curves, weakly-pseudo-stable curves and pseudo-stable curves, respectively.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v2122
606   $aAlgebraic geometry
606   $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019
615  0$aAlgebraic geometry.
615 14$aAlgebraic Geometry.
676   $a516.35
700   $aBini$b Gilberto$4aut$4http://id.loc.gov/vocabulary/relators/aut$0739663
702   $aFelici$b Fabio$4aut$4http://id.loc.gov/vocabulary/relators/aut
702   $aMelo$b Margarida$4aut$4http://id.loc.gov/vocabulary/relators/aut
702   $aViviani$b Filippo$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910299964903321
996   $aGeometric invariant theory for polarized curves$91465288
997   $aUNINA