The integral points and the special automorphism group of a surface
Abstract
We consider a smooth affine variety V defined by an irreducible polynomial f(x, y, z) = x2 + y2 − xyz − z over [special characters omitted]. We will describe all of its (rational) integral points via two automorphisms of V: one that is applied to the integral points of a twisted cubic curve lying on the surface with positive z-coordinates, and the other applied to one integral point on the surface with negative z-coordinate. Then we define the ‘special’ automorphism group of V to be the set of all automorphisms of V such that they can be lifted to automorphisms of [special characters omitted]. Then we will show that the special automorphism group of V is a Coxeter group of rank 3. Further we will generalize the surface and compute its special automorphism group.
Degree
Ph.D.
Advisors
Moh, Purdue University.
Subject Area
Mathematics
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