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Taking A Canon To The Adjunction Formula, Paul M. Harrelson
Taking A Canon To The Adjunction Formula, Paul M. Harrelson
Electronic Theses and Dissertations
In this paper, we show how the canonical divisor of a graph is related to the canonical divisor of its subgraph. The use of chip firing and the adjunction formula for graphs ex- plains said relation and even completes it. We go on to show the difference between the formula for full subgraphs and that of non-full subgraphs. Examples are used to simplify these results and to see the adjunction formula in action. Finally, we show that though the adjunction formula seems simple at first glance, it is somewhat complex and rather useful.
Automorphisms Of Graph Curves On K3 Surfaces, Joshua C. Ferrerra
Automorphisms Of Graph Curves On K3 Surfaces, Joshua C. Ferrerra
Electronic Theses and Dissertations
We examine the automorphism group of configurations of rational curves on $K3$ surfaces. We use the properties of finite automorphisms of $\PP^1$ to examine what restrictions a given elliptic fibration imposes on the possible finite order non-symplectic automorphisms of the $K3$ surface. We also examine the fixed loci of these automorphisms, and construct an explicit fibration to demonstrate the process.