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Structures On A K3 Surface, Nathan P. Rowe

UNLV Theses, Dissertations, Professional Papers, and Capstones

In the first part of this paper, we examine properties of K3 surfaces of the form:

(x2 + 1)(y2 + 1)(z2 + 1) + Axyz − 2 = 0

We show the surface has Picard number q " 12 by finding 12 curves whose equivalence classes are linearly independent. These curves have self intersection −2. We find the lattice representations of the single-coordinate swapping automorphisms in x, y, and z. We show that we have enough of the Lattice to make accurate predictions of polynomial degree growth under the automorphisms. We describe these automorphisms in terms of operations on elliptic …