New PDF release: Geometric Invariant Theory for Polarized Curves

By Gilberto Bini

ISBN-10: 3319113364

ISBN-13: 9783319113364

ISBN-10: 3319113372

ISBN-13: 9783319113371

We examine GIT quotients of polarized curves. extra in particular, we research the GIT challenge for the Hilbert and Chow schemes of curves of measure d and genus g in a projective house of measurement d-g, as d decreases with appreciate to g. We turn out that the 1st 3 values of d at which the GIT quotients switch are given through d=a(2g-2) the place a=2, 3.5, four. We exhibit that, for a>4, L. Caporaso's effects carry real for either 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 they usually map to the moduli stack of pseudo-stable curves. We additionally study intimately the severe values a=3.5 and a=4, the place the Hilbert semistable locus is precisely smaller than the Chow semistable locus. As an program, we receive 3 compactications of the common Jacobian over the moduli house of solid curves, weakly-pseudo-stable curves and pseudo-stable curves, respectively.

Show description

Read Online or Download Geometric Invariant Theory for Polarized Curves PDF

Best algebraic geometry books

Lectures on introduction to moduli problems and orbit spaces - download pdf or read online

Backbone identify: advent to moduli difficulties and orbit areas.

Download e-book for kindle: Higher-Dimensional Algebraic Geometry by Olivier Debarre

Higher-Dimensional Algebraic Geometry experiences the class thought of algebraic forms. This very energetic region of study continues to be constructing, yet an awesome volume of data has collected during the last two decades. The author's aim is to supply an simply available creation to the topic.

Download PDF by Constance Reid: Hilbert

Now in new alternate paper variations, those vintage biographies of 2 of the best twentieth Century mathematicians are being published less than the Copernicus imprint. those noteworthy money owed of the lives of David Hilbert and Richard Courant are heavily comparable: Courant's tale is, in lots of methods, visible because the sequel to the tale of Hilbert.

New PDF release: Foliation Theory in Algebraic Geometry

That includes a mix of unique learn papers and entire surveys from a global workforce of prime researchers within the thriving fields of foliation thought, holomorphic foliations, and birational geometry, this publication provides the lawsuits of the convention "Foliation conception in Algebraic Geometry," hosted by means of the Simons origin in long island urban in September 2013.

Extra resources for Geometric Invariant Theory for Polarized Curves

Example text

Therefore, the closed points of Mg are the wpstable curves X such that every elliptic tail of X is cuspidal and every cusp of X is contained in an elliptic tail. 4 are indeed good moduli spaces (see [Alp2, Prop. 4]). Y /, by contracting the elliptic tails of Y to cusps. The p-stable reduction works even for families. 20 2 Singular Curves X Z E p q elliptic tail C pinched to an ordinary cusp at q C Y p q R C cuspidal elliptic tail wp Fig. e. 6 Let v W Y ! S be a family of wp-stable curves of genus g There exists a commutative diagram 2.

W /c j. W /. Part (ii): start by noticing that if every exceptional component E Z which is contracted by is also contracted by 0 , then 0 factors through , so the map exists. Let us now prove that in order for the map to exist, it is also necessary that every exceptional component E Z which is contracted by is also contracted by 0 . By contradiction, assume that exists and that there exists an exceptional component E Z which is contracted by but not by 0 . E 0 / is an exceptional component of Y and that d 0 is properly balanced.

4]. In what follows, we will show how to adapt the argument of loc. cit. in order to work out in our case. 1 in [HH09], which asserts that given a stable curve C , there is a replacement morphism C W C ! 1 Stable, p-Stable and wp-Stable Curves 21 cusps. The argumentation is local on the nodes connecting each genus-one subcurve meeting the rest of the curve in a single node. Since in a wp-stable curve all elliptic tails are connected to the rest of the curve via a single node, the same argumentation works also in our case with no further modifications.

Download PDF sample

Geometric Invariant Theory for Polarized Curves by Gilberto Bini

by Steven

Rated 4.76 of 5 – based on 18 votes

Categories: Algebraic Geometry