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The cohomology of Kontesevich’s stack of stable maps to Pⁿ, the case of conics O’Halloran, Anne Fionnuala
Abstract
In this thesis we consider the singular cohomology of M₀,₀(Pⁿ,2), the coarse moduli space associated to Kontsevich's stack of degree two stable maps to Pⁿ, M₀,₀(Pⁿ,2). We show that the cohomology ring is generated by a divisor d which corresponds to the locus of pairs (C,g) with C reducible, and the first and second Chern classes, c₁ and c₂, of the canonical rank three vector bundle E = π۰f0(1) on M₀,₀(Pⁿ,2), where π is the canonical projection associated to the universal curve C and f is the universal map. We give the cohomology ring as a quotient of a polynomial ring in these generators. The relations are in degrees n, n + 1 and n + 2. We also give a representation of the cohomology ring in terms of the Chern roots of E. The results are conjectural for n >> 0.
Item Metadata
Title |
The cohomology of Kontesevich’s stack of stable maps to Pⁿ, the case of conics
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2000
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Description |
In this thesis we consider the singular cohomology of M₀,₀(Pⁿ,2), the coarse moduli space associated to Kontsevich's stack of degree two stable maps to Pⁿ, M₀,₀(Pⁿ,2). We show that the cohomology ring is generated by a divisor d which corresponds to the locus of pairs (C,g) with C reducible, and the first and second Chern classes, c₁ and c₂, of the canonical rank three vector bundle E = π۰f0(1) on M₀,₀(Pⁿ,2), where π is the canonical projection associated to the universal curve C and f is the universal map. We give the cohomology ring as a quotient of a polynomial ring in these generators. The relations are in degrees n, n + 1 and n + 2. We also give a representation of the cohomology ring in terms of the Chern roots of E. The results are conjectural for n >> 0.
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Extent |
5012796 bytes
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File Format |
application/pdf
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Language |
eng
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Date Available |
2009-09-25
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0080018
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2000-11
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.