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arXiv · 1502.00275

On minimal rational elliptic surfaces

Antonio Laface·Damiano Testa
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Abstract

We construct $13$ projective $\mathbb{Q}$-factorial Fano toric varieties and show that for any minimal rational elliptic surface $X$ there is one such toric variety $Z_X$ and a divisor class $δ_X\in {\rm Cl}(Z_X)$ such that the number of $(-1)$-curves of $X$ equals the dimension of the Riemann-Roch space of $δ_X$. As an application we give the number of $(-1)$-curves of any such elliptic fibration of Halphen index $2$.

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Antonio Laface, Damiano Testa. 2015-05-10. On minimal rational elliptic surfaces. https://arxiv.org/abs/1502.00275

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