十六阶皮卡德广义四次元上的雅可比椭圆颤振

Albanian journal of mathematics Pub Date : 2023-06-15 DOI:10.51286/albjm/1675936273

Adrian Clingher, Thomas Hill, Andreas Malmendier

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引用次数: 1

摘要

考虑一类具有Picard格的复代数K3曲面，其中包含单模格H⊕E7(−1)⊕E7(−1)。曲面f (f)允许一个与四次超曲面同构的双态模型，它推广了Inose四次曲面。我们证明了这个族的一个一般成员有四个不相等的雅可比椭圆纤支，并构造了它们的显式铅笔。

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JACOBIAN ELLIPTIC FIBRATIONS ON THE GENERALIZED INOSE QUARTIC OF PICARD RANK SIXTEEN

We consider the family of complex algebraic K3 surfaces 𝒳 with Picard lattice containing the unimodular lattice H⊕E7(−1)⊕E7(−1). The surface 𝒳 admits a birational model isomorphic to a quartic hypersurface that generalizes the Inose quartic. We prove that a general member of this family admits exactly four inequivalent Jacobian elliptic fibrations and construct explicit pencils for them.

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Albanian journal of mathematics

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