Pseudolattices, del Pezzo surfaces, and Lefschetz fibrations

Harder, Andrew; Thompson, Alan

doi:10.1090/tran/7960

Pseudolattices, del Pezzo surfaces, and Lefschetz fibrations
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by Andrew Harder and Alan Thompson PDF

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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 $1$ Lefschetz fibrations over discs.

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