You might also like

More about Geometric Invariant Theory for Polarized Curves

• Book details
• Synopsis
• Trending among others

You get 140 loyalty points

Book synopsis

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 a4, 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.§

Book details

Book category Książki po angielsku Mathematics & science Mathematics Geometry

• Full title: Geometric Invariant Theory for Polarized Curves
• Author: Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani
• Language: English
• Binding: Paperback
• Number of pages: 211
• EAN: 9783319113364
• ISBN: 3319113364
• ID: 05267117
• Publisher: Springer International Publishing AG
• Weight: 349 g
• Dimensions: 235 × 155 × 235 mm
• Date of publishing: 08. November 2014

Trending among others

---

---

---