Barlow, Rebecca Nora (1982) Some new surfaces with pg = 0. PhD thesis, University of Warwick.

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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 or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Surfaces
Official Date:	September 1982
Dates:	Date Event September 1982 Submitted
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Publication Status:	Unpublished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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