@article{7ee80486c8b844d9a32de0b982e9c2df,

title = "Pseudolattices, del pezzo surfaces, and lefschetz fibrations",

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.",

author = "Andrew Harder and Alan Thompson",

note = "Funding Information: Received by the editors September 17, 2018, and, in revised form, May 7, 2019, and July 28, 2019. 2010 Mathematics Subject Classification. Primary 14F05; Secondary 14D05, 14J26, 18F30, 53D37, 57R17. The first author was partially supported by the Simons Collaboration Grant in “Homological Mirror Symmetry”. The second author was partially supported by the Engineering and Physical Sciences Research Council program grant “Classification, Computation, and Construction: New Methods in Geometry”. The idea for this paper arose following discussions between Charles Doran and the authors during a visit to the Harvard Center of Mathematical Sciences and Applications (CMSA) in April 2018; the authors would like to thank the CMSA for their kind hospitality.",

year = "2020",

doi = "10.1090/tran/7960",

language = "English (US)",

volume = "373",

pages = "2071--2104",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "3",

}