Exceptional sequences of invertible sheaves on rational surfaces

被引：47
作者：
Hille, Lutz [1 ]
Perling, Markus [2 ]
机构：
[1] Univ Munster, Inst Math, Fachbereich Math & Informat, D-48149 Munster, Germany
[2] Ruhr Univ Bochum, Fak Math, D-44780 Bochum, Germany
来源：
COMPOSITIO MATHEMATICA | 2011年 / 147卷 / 04期
关键词：
toric surfaces; rational surfaces; derived categories; exceptional sequences; DEL PEZZO SURFACES; COHERENT SHEAVES; HOMOGENEOUS SPACES; PROJECTIVE BUNDLES; TORIC VARIETIES; MODULI SPACES; CATEGORIES; ALGEBRAS; HELICES; COLLECTIONS;
D O I：
10.1112/S0010437X10005208
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article we consider exceptional sequences of invertible sheaves on smooth complete rational surfaces. We show that to every such sequence one can associate a smooth complete toric surface in a canonical way. We use this structural result to prove various theorems on exceptional and strongly exceptional sequences of invertible sheaves on rational surfaces. We construct full strongly exceptional sequences for a large class of rational surfaces. For the case of toric surfaces we give a complete classification of full strongly exceptional sequences of invertible sheaves.
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页码：1230 / 1280
页数：51
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