@article{86cb6b5ac5384375924d1955a9bf7ee4,
title = "Birational modifications of surfaces via unprojections",
abstract = "We describe elementary transformations between minimal models of rational surfaces in terms of unprojections. These do not fit into the framework of Kustin-Miller unprojections as introduced by Papadakis and Reid, since we have to leave the world of projectively Gorenstein varieties. Also, our unprojections do not depend on the choice of the unprojection locus only, but need extra data corresponding to the choice of a divisor on this unprojection locus.",
keywords = "Birational geometry of surfaces, Elementary transformation, Hirzebruch surface, Kustin-Miller unprojection",
author = "Christian Liedtke and Papadakis, {Stavros Argyrios}",
note = "Funding Information: We thank Francesco Zucconi and the referee for remarks, comments and pointing out a couple of inaccuracies. Stavros Papadakis is a participant of the Project PTDC/MAT/099275/2008, a member of CAMSGD (IST/UTL), and gratefully acknowledges funding from the Portuguese Funda{\c c}{\~a}o para a Ci{\^e}ncia e a Tecnologia (FCT) under research grant SFRH/BPD/22846/2005 of POCI2010/FEDER. Much of this work was done while he was visiting the university of D{\"u}sseldorf. We thank the Mathematisches Institut and the DFG-Forschergruppe Classification of Algebraic Surfaces and Compact Complex Manifolds for the kind hospitality and financial support.",
year = "2010",
month = may,
day = "1",
doi = "10.1016/j.jalgebra.2010.02.032",
language = "English",
volume = "323",
pages = "2510--2519",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",
number = "9",
}