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arXiv · 1808.06345

Pseudolattices, del Pezzo surfaces, and Lefschetz fibrations

Andrew Harder·Alan Thompson
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Abstract

Motivated by the relationship between numerical Grothendieck groups induced by the embedding of a smooth anticanonical elliptic curve into a del Pezzo surface, we define the notion of a quasi del Pezzo homomorphism between pseudolattices and establish its basic properties. The primary aim of the paper is then to prove a classification theorem for quasi del Pezzo homomorphisms, using a pseudolattice variant of the minimal model program. Finally, this result is applied to the classification of a certain class of genus one Lefschetz fibrations over discs.

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Andrew Harder, Alan Thompson. 2018-08-20. Pseudolattices, del Pezzo surfaces, and Lefschetz fibrations. https://doi.org/10.1090/tran/7960

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