Ulrich bundles on ruled surfaces

被引：27

作者：

Aprodu, Marian ^{[1
,2
]}

Costa, Laura ^{[3
]}

Maria Miro-Roig, Rosa ^{[3
]}

机构：

[1] Univ Bucuresti, Fac Matemat & Informat, Str Acad 14, Bucharest 010014, Romania

[2] Acad Romane, Inst Matemat Simion Stoilow, Calea Grivitei 21,Sect 1, Bucharest 010702, Romania

[3] Fac Matemat & Informat, Dept Matemat & Informat, Gran Via Corts Catalanes 585, Barcelona 08007, Spain

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2018年 / 222卷 / 01期

关键词：

REPRESENTATION TYPE;

D O I：

10.1016/j.jpaa.2017.03.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this short note, we study the existence problem for Ulrich bundles on polarized ruled surfaces, focusing our attention on the smallest possible rank. We show that existence of Ulrich line bundles occurs if and only if the coefficient a of the minimal section in the numerical class of the polarization equals one. For other polarizations, we prove the existence of rank two Ulrich bundles. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：131 / 138

页数：8

共 18 条

[1]

Aprodu M., 2017, ANN U FERRA IN PRESS

[2] Minimal resolutions, Chow forms and Ulrich bundles on K3 surfaces [J].

Aprodu, Marian ;

Farkas, Gavril ;

Ortega, Angela .

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2017, 730 :225-249

[3]

Beauville A, 2000, MICH MATH J, V48, P39

[4]

Beauville A., ARXIV 1607 00895

[5] STABLE ULRICH BUNDLES [J].

Casanellas, Marta ;

Hartshorne, Robin ;

Geiss, Florian ;

Schreyer, Frank-Olaf .

INTERNATIONAL JOURNAL OF MATHEMATICS, 2012, 23 (08)

[6]

Coskun E, 2012, DOC MATH, V17, P1003

[7] The geometry of Ulrich bundles on del Pezzo surfaces [J].

Coskun, Emre ;

Kulkarni, Rajesh S. ;

Mustopa, Yusuf .

JOURNAL OF ALGEBRA, 2013, 375 :280-301

[8] Ulrich Schur bundles on flag varieties [J].

Coskun, Izzet ;

Costa, Laura ;

Huizenga, Jack ;

Maria Miro-Roig, Rosa ;

Woolf, Matthew .

JOURNAL OF ALGEBRA, 2017, 474 :49-96

[9]

Costa L, 2015, MATH ANN, V361, P443, DOI 10.1007/s00208-014-1076-9

[10] The representation type of Segre varieties [J].

Costa, Laura ;

Miro-Roig, Rosa M. ;

Pons-Llopis, Joan .

ADVANCES IN MATHEMATICS, 2012, 230 (4-6) :1995-2013

← 1 2 →