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The Geometry of Stable Quotients in ...

Cooper, Yaim.

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The Geometry of Stable Quotients in Genus One.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	The Geometry of Stable Quotients in Genus One./
作者:	Cooper, Yaim.
面頁冊數:	51 p.
附註:	Source: Dissertation Abstracts International, Volume: 74-09(E), Section: B.
Contained By:	Dissertation Abstracts International74-09B(E).
標題:	Mathematics. -
電子資源:	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.
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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.
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