Geometric Invariant Theory for Polarized Curves
Bini, Gilberto.
Geometric Invariant Theory for Polarized Curves [electronic resource] / by Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani. - X, 211 p. 17 illus. online resource. - Lecture Notes in Mathematics, 2122 0075-8434 ; . - Lecture Notes in Mathematics, 2122 .
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
9783319113371
10.1007/978-3-319-11337-1 doi
Geometry, algebraic.
Algebraic Geometry.
QA564-609
516.35
Geometric Invariant Theory for Polarized Curves [electronic resource] / by Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani. - X, 211 p. 17 illus. online resource. - Lecture Notes in Mathematics, 2122 0075-8434 ; . - Lecture Notes in Mathematics, 2122 .
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
9783319113371
10.1007/978-3-319-11337-1 doi
Geometry, algebraic.
Algebraic Geometry.
QA564-609
516.35