Exceptional collections on Dolgachev surfaces associated with degenerations

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Dolgachev surfaces are simply connected minimal elliptic surfaces with p(g) = q = 0 and of Kodaira dimension 1. These surfaces are constructed by logarithmic transformations of rational elliptic surfaces. In this paper, we explain the construction of Dolgachev surfaces via Q-Gorenstein smoothing of singular rational surfaces with two cyclic quotient singularities. This construction is based on the paper [25]. Also, some exceptional bundles on Dolgachev surfaces associated with Q-Gorenstein smoothing have been constructed based on the idea of Hacking [12]. In the case if Dolgachev surfaces were of type (2,3), we describe the Picard group and present an exceptional collection of maximal length. Finally, we prove that the presented exceptional collection is not full, hence there exists a nontrivial phantom category in the derived category. (C) 2017 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2018-01
Language
English
Article Type
Article
Keywords

GENERAL TYPE; ALGEBRAIC-SURFACES; ENRIQUES SURFACES; VECTOR-BUNDLES; LINE BUNDLES; SINGULARITIES; CATEGORIES; DEFORMATIONS

Citation

ADVANCES IN MATHEMATICS, v.324, pp.394 - 436

ISSN
0001-8708
DOI
10.1016/j.aim.2017.11.012
URI
http://hdl.handle.net/10203/239451
Appears in Collection
MA-Journal Papers(저널논문)
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