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Moduli Spaces of Dynamical Systems o...
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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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Source: Dissertation Abstracts International, Volume: 72-07, Section: B, page: .
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Adviser: Shou-Wu Zhang.
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Thesis (Ph.D.)--Columbia University, 2011.
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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
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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.
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School code: 0054.
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http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3454090
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