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Moduli Spaces of Dynamical Systems o...

Levy, Alon.

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Moduli Spaces of Dynamical Systems on Pn.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Moduli Spaces of Dynamical Systems on Pn./
Author:	Levy, Alon.
Description:	73 p.
Notes:	Source: Dissertation Abstracts International, Volume: 72-07, Section: B, page: .
Contained By:	Dissertation Abstracts International72-07B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3454090
ISBN:	9781124628516

Moduli Spaces of Dynamical Systems on Pn.
Levy, Alon.

Moduli Spaces of Dynamical Systems on Pn. - 73 p.

Source: Dissertation Abstracts International, Volume: 72-07, Section: B, page: .

Thesis (Ph.D.)--Columbia University, 2011.

This thesis studies the space of morphisms on Pn defined by polynomials of degree d and its quotient by the conjugation action of PGL(n + 1), which should be thought of as coordinate change. First, we construct the quotient using geometric invariant theory, proving that it is a geometric quotient and that the stabilizer group in PGL(n + 1) of each morphism is finite and bounded in terms of n and d. We then show that when n = 1, the quotient space is rational over a field of any characteristic.

ISBN: 9781124628516Subjects--Topical Terms:

515831
Mathematics.

Moduli Spaces of Dynamical Systems on Pn.
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020 $a 9781124628516
035 $a (UMI)AAI3454090
035 $a AAI3454090
040 $a UMI $c UMI
100 1 $a Levy, Alon. $3 1684291
245 1 0 $a Moduli Spaces of Dynamical Systems on Pn.
300 $a 73 p.
500 $a Source: Dissertation Abstracts International, Volume: 72-07, Section: B, page: .
500 $a Adviser: Shou-Wu Zhang.
502 $a Thesis (Ph.D.)--Columbia University, 2011.
520 $a This thesis studies the space of morphisms on Pn defined by polynomials of degree d and its quotient by the conjugation action of PGL(n + 1), which should be thought of as coordinate change. First, we construct the quotient using geometric invariant theory, proving that it is a geometric quotient and that the stabilizer group in PGL(n + 1) of each morphism is finite and bounded in terms of n and d. We then show that when n = 1, the quotient space is rational over a field of any characteristic.
520 $a We then study semistable reduction in this space. For every complete curve C in the semistable completion of the quotient space, we can find curves upstairs mapping down to it; this leads to an abstract complete curve D with a projective vector bundle parametrizing maps on the curve. The bundle is trivial iff there exists a complete curve D in the semistable space upstairs mapping down to C; we show that for every n and d we can find a C for which no such D exists. Finally, in the case where D does exist, we show that, whenever it lies in the stable space, the map from D to C is ramified only over points with unusually large stabilizer, which for a fixed rational C will bound the degree of the map from D to C.
590 $a School code: 0054.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical Mathematics. $3 1672766
690 $a 0405
690 $a 0642
710 2 $a Columbia University. $b Mathematics. $3 1684292
773 0 $t Dissertation Abstracts International $g 72-07B.
790 1 0 $a Zhang, Shou-Wu, $e advisor
790 $a 0054
791 $a Ph.D.
792 $a 2011
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3454090