Dicks, Duncan (1988) Surfaces with pg = 3 and K2 = 4 and extension-deformation theory. PhD thesis, University of Warwick.

Preview

PDF WRAP_Theses_Dicks_1988.pdf - Submitted Version - Requires a PDF viewer. Download (2543Kb) | Preview

Request Changes to record.

Abstract

In Chapter 2 we give a description of an algorithm suggested by Reid for studying extensions of a variety C⊂P^n as a hyperplane section of a variety in P^(n+1).

In Chapter 3 we use this method to study surfaces with numerical invariants P_g = 3 and K² = 4. We find that there are 5 families of such surfaces and produce explicitly the canonical ring for a generic member of each family. In [Ho 1] there is a geometric study of surfaces with these invariants.

Proposition (15.2) is an example of an obstruction to the extension deformation algorithm which appears in degree 4.

In Chapter 4 we write down some one parameter deformations between the families. We conjecture that there are no degenerations, II → 〖III〗_(a ) or II →〖III〗_b. We draw some geometric conclusions, from the algebraic descriptions, about the branch locus of surfaces of type III, 〖III〗_(a )and 〖III〗_bas double covers of P² [Ho1]. It is also shown that a surface of type II is the resolution of a numerical quintic with an elliptic Gorenstein singularity of type k = 1.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Surfaces, Rings (Algebra), Algebraic varieties, Surfaces, Deformation of
Official Date:	September 1988
Dates:	Date Event September 1988 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Reid, Miles (Miles A.)
Sponsors:	Science and Engineering Research Council (Great Britain)
Format of File:	pdf
Extent:	125 leaves
Language:	eng

Request changes or add full text files to a record

Repository staff actions (login required)

View Item

Downloads