Hilbert Modular Threefolds of Arithmetic Genus One |
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| Authors: | HG GrundmanLE Lippincott |
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| Institution: | Department of Mathematics, Bryn Mawr College, Bryn Mawr, Pennsylvania, 19010, f1grundman@brynmawr.eduf1, f2llippinc@noether.brynmawr.eduf2 |
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| Abstract: | In 1981, Weisser proved that there are exactly four Galois cubic number fields with Hilbert modular threefolds of arithmetic genus one. In this paper, we extend Weisser's work to cover all cubic number fields. Our main result is that there are exactly 33 fields with Hilbert modular threefolds of arithmetic genus one. These fields are enumerated explicitly. |
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| Keywords: | threefolds varieties modular arithmetic genus Hilbert rational |
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