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The Geometry of Stable Quotients in ...

Cooper, Yaim.

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The Geometry of Stable Quotients in Genus One.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	The Geometry of Stable Quotients in Genus One./
Author:	Cooper, Yaim.
Description:	51 p.
Notes:	Source: Dissertation Abstracts International, Volume: 74-09(E), Section: B.
Contained By:	Dissertation Abstracts International74-09B(E).
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3562278
ISBN:	9781303098406

The Geometry of Stable Quotients in Genus One.
Cooper, Yaim.

The Geometry of Stable Quotients in Genus One. - 51 p.

Source: Dissertation Abstracts International, Volume: 74-09(E), Section: B.

Thesis (Ph.D.)--Princeton University, 2013.

Stable quotients provide an alternative to stable maps for compactifying spaces of maps. When n ≥ 2, the space Q¯g( Pn-1 , d) = Q¯g( G(1, n), d) compactifies the space of degree d maps of smooth genus g curves to Pn-1 , while Q¯g(G(1, 1), d) &sime; M¯1, d·epsilon/Sd is a quotient of a Hassett weighted pointed space. In this paper we study the coarse moduli schemes associated to the smooth proper Deligne-Mumford stacks Q¯ 1( Pn-1 ), for all n ≥ 1. We show these schemes are projective, unirational, and have Picard number 2. Then we give generators for the Picard group, compute the canonical divisor, and the cones of ample and effective divisors. We conclude that Q¯1( Pn-1 , d) is Fano if and only if n( d - 1)(d + 2) < 20. Moreover, we show that Q¯1( Pn-1 , d) is a Mori Fiber space for all n, d, hence always minimal in the sense of the minimal model program. In the case n = 1, we write in addition a closed formula for the Poincare polynomial.

ISBN: 9781303098406Subjects--Topical Terms:

515831
Mathematics.

The Geometry of Stable Quotients in Genus One.
LDR:01853nam a2200277 4500 001 1964698
005 20141010092805.5
008 150210s2013 ||||||||||||||||| ||eng d
020 $a 9781303098406
035 $a (MiAaPQ)AAI3562278
035 $a AAI3562278
040 $a MiAaPQ $c MiAaPQ
100 1 $a Cooper, Yaim. $3 2101196
245 1 4 $a The Geometry of Stable Quotients in Genus One.
300 $a 51 p.
500 $a Source: Dissertation Abstracts International, Volume: 74-09(E), Section: B.
500 $a Adviser: Rahul Pandharipande.
502 $a Thesis (Ph.D.)--Princeton University, 2013.
520 $a Stable quotients provide an alternative to stable maps for compactifying spaces of maps. When n ≥ 2, the space Q¯g( Pn-1 , d) = Q¯g( G(1, n), d) compactifies the space of degree d maps of smooth genus g curves to Pn-1 , while Q¯g(G(1, 1), d) &sime; M¯1, d·epsilon/Sd is a quotient of a Hassett weighted pointed space. In this paper we study the coarse moduli schemes associated to the smooth proper Deligne-Mumford stacks Q¯ 1( Pn-1 ), for all n ≥ 1. We show these schemes are projective, unirational, and have Picard number 2. Then we give generators for the Picard group, compute the canonical divisor, and the cones of ample and effective divisors. We conclude that Q¯1( Pn-1 , d) is Fano if and only if n( d - 1)(d + 2) < 20. Moreover, we show that Q¯1( Pn-1 , d) is a Mori Fiber space for all n, d, hence always minimal in the sense of the minimal model program. In the case n = 1, we write in addition a closed formula for the Poincare polynomial.
590 $a School code: 0181.
650 4 $a Mathematics. $3 515831
650 4 $a Applied Mathematics. $3 1669109
690 $a 0405
690 $a 0364
710 2 $a Princeton University. $b Mathematics. $3 2049791
773 0 $t Dissertation Abstracts International $g 74-09B(E).
790 $a 0181
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3562278