Hassett, Brendan E.2013-03-082013-03-082011Li, Shuijing. "Rational points on del Pezzo surfaces of degree 1 and 2." (2011) Diss., Rice University. <a href="https://hdl.handle.net/1911/70318">https://hdl.handle.net/1911/70318</a>.https://hdl.handle.net/1911/70318One 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.85 p.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Pure sciencesDel Pezzo surfacesAlgebraic geometryMathematicsThesisLiShuTHESIS MATH. 2011 LI