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Some new surfaces with pg = 0
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Barlow, Rebecca Nora (1982) Some new surfaces with pg = 0. PhD thesis, University of Warwick.
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WRAP_THESIS_Barlow_1982.pdf - Submitted Version Download (23Mb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b1755284~S1
Abstract
We give families of examples of surfaces of general type X with pg=0, K2=1 double covered by surfaces T with pg=0, K2=2.
In Chapter 2 we classify all such constructions with |π(T)|=8, giving 4-parameter families of surfaces X for which π(X)=Z2 and Z4. There is a complete description of surfaces with pg=0, K2=l, π=Z4 in [Rl]. There was one example S with H(S,Z)=Z2 in [0&P]. The most interesting construction is the one in Chapter 3, for which πX={l}. This answers negatively the following question "are all simply connected surfaces with pg=0 K2>0 rational" coming from Severi's conjecture.
These constructions were motivated by Reid's conjecture that if a given fundamental group H occurs, there should be examples X=T/Z2 with π(X)=H.
In the Appendix we give an alternative proof of a formula for the arithmetic genus of a quotient surface, based on a remark of Hirzebruch.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Surfaces | ||||
Official Date: | September 1982 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Reid, Miles (Miles A.) | ||||
Sponsors: | Science Research Council (Great Britain) (SRC) | ||||
Extent: | vii, 90 p. | ||||
Language: | eng |
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