Counting points of bounded height on del Pezzosurfaces

Mathematics;del Pezzo surfaces;rational points;height function

Kleven, Stephanie

University of Waterloo

关键词: Mathematics;    del Pezzo surfaces;    rational points;    height function;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/2948/1/sjfkleve2006.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

del Pezzo surfaces are isomorphic to either P¹ x P¹ or P² blown up a times, wherea ranges from 0 to 8. We will look at lines on del Pezzo surfaces isomorphic to P² blown up atimes with a ranging from 0 to 6. We will show that when we count points of bounded heighton one of these surfaces, the number of points on lines give us the primary growthorder, but the secondary growth order calculates the number of points on the restof the surface and hence is a better representation of the geometry of the surface.