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<p>We discuss the role of hyperelliptic fibrations in F-theory. For each even integer <i>n</i> we give a noncompact Calabi-Yau threefold <i>X</i> containing a hyperelliptically fibered surface <i>Y</i>, such that <i>X</i> and <i>Y</i> are homotopy equivalent and <i>c</i><sub>2</sub>(<i>X</i>) = <i>n</i>. We investigate two distinct cases depending on the position of the hyperelliptic fibration. First, we propose to extend F-theory considering hyperelliptic fibrations, giving an identification between the determinant of the period matrix and the axio-dilaton. Such an identification requires that the curve satisfies an appropriate criterium which we describe. Our explicit examples have split Jacobian, preserve the same number of degrees of freedom of usual F-theory while allowing for the appearance of a greater variety of singularities. Second, when the hyperelliptic fibration is contained in the base of a Calabi-Yau fourfold, we show that tadpole cancellation conditions are satisfied for arbitrarily large values of <i>c</i><sub>2</sub>(<i>X</i>).</p>

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F-theory with hyperelliptic fibrations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月4日

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  • E. Ballico,
  • M. P. García del Moral,
  • E. Gasparim,
  • C. las Heras

摘要

We discuss the role of hyperelliptic fibrations in F-theory. For each even integer n we give a noncompact Calabi-Yau threefold X containing a hyperelliptically fibered surface Y, such that X and Y are homotopy equivalent and c2(X) = n. We investigate two distinct cases depending on the position of the hyperelliptic fibration. First, we propose to extend F-theory considering hyperelliptic fibrations, giving an identification between the determinant of the period matrix and the axio-dilaton. Such an identification requires that the curve satisfies an appropriate criterium which we describe. Our explicit examples have split Jacobian, preserve the same number of degrees of freedom of usual F-theory while allowing for the appearance of a greater variety of singularities. Second, when the hyperelliptic fibration is contained in the base of a Calabi-Yau fourfold, we show that tadpole cancellation conditions are satisfied for arbitrarily large values of c2(X).