LEADER 03037nam a2200373 i 4500 001 991002955089707536 008 160728s2014 sz a b 001 0 eng d 020 $a9783319113364 035 $ab14259990-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a516.35$223 084 $aAMS 14L24 084 $aAMS 14B05 084 $aAMS 14C05 084 $aAMS 14C25 084 $aLC QA564.B485 245 00$aGeometric invariant theory for polarized curves /$cGilberto Bini ... [et al.] 260 $aCham [Switzerland] :$bSpringer,$cc2014 300 $ax, 211 p. :$bill. ;$c24 cm 440 0$aLecture notes in mathematics,$x0075-8434 ;$v2122 504 $aIncludes bibliographical references and index 505 0 $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 520 $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