Abstract
We describe elliptic models with section on the Shioda supersingular K3 surface X of Artin invariant 1 over an algebraically closed field of characteristic 3. We compute elliptic parameters and Weierstrass equations for the fifty two different fibrations, and analyze some of the reducible fibers and Mordell-Weil lattices.
The author thanks his thesis advisor Prof. Abhinav Kumar for his precious guidance. And also the mathematics departments of Brandeis University, Massachusetts Institute of Technology and University of Hyderabad for invaluable help during the period of this project.
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Acknowledgements
I thank Abhinav Kumar and Noam Elkies for many helpful discussions and suggestions. The computer algebra systems PARI/gp and Maxima were used in the calculations for this paper. I thank the developers of these programs.
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Sengupta, T. (2017). Elliptic Fibrations on Supersingular K3 Surface with Artin Invariant 1 in Characteristic 3. In: Aryasomayajula, A., Biswas, I., Morye, A.S., Parameswaran, A.J. (eds) Analytic and Algebraic Geometry. Springer, Singapore. https://doi.org/10.1007/978-981-10-5648-2_15
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DOI: https://doi.org/10.1007/978-981-10-5648-2_15
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