03908nam 22006255 450 991029996490332120200630173607.03-319-11337-210.1007/978-3-319-11337-1(CKB)3710000000306132(SSID)ssj0001386506(PQKBManifestationID)11884091(PQKBTitleCode)TC0001386506(PQKBWorkID)11373753(PQKB)10135939(DE-He213)978-3-319-11337-1(MiAaPQ)EBC6301270(MiAaPQ)EBC5588030(Au-PeEL)EBL5588030(OCoLC)895007525(PPN)183094387(EXLCZ)99371000000030613220141107d2014 u| 0engurnn#008mamaatxtccrGeometric Invariant Theory for Polarized Curves /by Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani1st ed. 2014.Cham :Springer International Publishing :Imprint: Springer,2014.1 online resource (X, 211 p. 17 illus.)Lecture Notes in Mathematics,0075-8434 ;2122Bibliographic Level Mode of Issuance: Monograph3-319-11336-4 Includes bibliographical references and index.Introduction -- 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.  .We 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.Lecture Notes in Mathematics,0075-8434 ;2122Algebraic geometryAlgebraic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11019Algebraic geometry.Algebraic Geometry.516.35Bini Gilbertoauthttp://id.loc.gov/vocabulary/relators/aut739663Felici Fabioauthttp://id.loc.gov/vocabulary/relators/autMelo Margaridaauthttp://id.loc.gov/vocabulary/relators/autViviani Filippoauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910299964903321Geometric invariant theory for polarized curves1465288UNINA