000			03614nam a22004815i 4500
001			978-3-319-11337-1
003			DE-He213
005			20190213151040.0
007			cr nn 008mamaa
008			141107s2014 gw | s |||| 0|eng d
020			_a9783319113371 _9978-3-319-11337-1
024	7		_a10.1007/978-3-319-11337-1 _2doi
050		4	_aQA564-609
072		7	_aPBMW _2bicssc
072		7	_aMAT012010 _2bisacsh
072		7	_aPBMW _2thema
082	0	4	_a516.35 _223
100	1		_aBini, Gilberto. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut
245	1	0	_aGeometric Invariant Theory for Polarized Curves _h[electronic resource] / _cby Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani.
264		1	_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2014.
300			_aX, 211 p. 17 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aLecture Notes in Mathematics, _x0075-8434 ; _v2122
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<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.
650		0	_aGeometry, algebraic.
650	1	4	_aAlgebraic Geometry. _0http://scigraph.springernature.com/things/product-market-codes/M11019
700	1		_aFelici, Fabio. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut
700	1		_aMelo, Margarida. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut
700	1		_aViviani, Filippo. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783319113388
776	0	8	_iPrinted edition: _z9783319113364
830		0	_aLecture Notes in Mathematics, _x0075-8434 ; _v2122
856	4	0	_uhttps://doi.org/10.1007/978-3-319-11337-1
912			_aZDB-2-SMA
912			_aZDB-2-LNM
999			_c9334 _d9334