One of the fundamental problems in Algebraic Geometry is to study solutions to certain systems of polynomial equations in several variables, or in other words, find rational points on a given variety which is defined by equations. In this paper, we discuss the existence of del Pezzo surface of degree 1 and 2 with a unique rational point over any finite field [Special characters omitted.] , and we will give a lower bound on the number of rational points to each q. Furthermore, we will give explicit equations of del Pezzo surfaces with a unique rational point. Also we will discuss the rationality property of the del Pezzo surfaces especially in lower degrees.
| Identifer | oai:union.ndltd.org:RICE/oai:scholarship.rice.edu:1911/70318 |
| Date | January 2011 |
| Contributors | Hassett, Brendan |
| Source Sets | Rice University |
| Language | English |
| Detected Language | English |
| Type | Thesis, Text |
| Format | 85 p., application/pdf |
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