Ulrich bundles on cubic fourfolds

被引：4

作者：

Faenzi, Daniele ^{[1
]}

Kim, Yeongrak ^{[2
]}

机构：

[1] Univ Bourgogne & Franche Comte, UMR 5584, CNRS, Inst Math Bourgogne, 9 Ave Alain Savary,BP 47870, F-21078 Dijon, France

[2] Pusan Natl Univ, Dept Math, 2 Busandaehak Ro 63beon Gil, Busan 46241, South Korea

来源：

COMMENTARII MATHEMATICI HELVETICI | 2022年 / 97卷 / 04期

关键词：

Ulrich bundles; cubic fourfolds; Kuznetsov category; MODULI SPACE; ACM BUNDLES;

D O I：

10.4171/CMH/546

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show the existence of rank 6 Ulrich bundles on a smooth cubic fourfold. First, we construct a simple sheaf E of rank 6 as an elementary modification of an ACM bundle of rank 6 on a smooth cubic fourfold. Such an E appears as an extension of two Lehn-Lehn-Sorger-van Straten sheaves. Then we prove that a general deformation of E(1) becomes Ulrich. In particular, this says that general cubic fourfolds have Ulrich complexity 6.

引用

页码：691 / 728

页数：38

共 50 条

[1] Stable Ulrich bundles on cubic fourfolds
Hoang, Truong Le
Hoang, Yen Ngoc
[J]. MANUSCRIPTA MATHEMATICA, 2023, 174 (1-2) : 243 - 267
[2] Ulrich bundles on special cubic fourfolds of small discriminants
Kim, Yeongrak
[J]. JOURNAL OF ALGEBRA, 2024, 660 : 398 - 422
[3] REMARKS ON ULRICH BUNDLES OF SMALL RANKS OVER QUARTIC FOURFOLDS
Kim, Yeongrak
[J]. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2024, 61 (02) : 279 - 291
[4] Special cubic fourfolds
Hassett, B
[J]. COMPOSITIO MATHEMATICA, 2000, 120 (01) : 1 - 23
[5] Serre-invariant stability conditions and Ulrich bundles on cubic threefolds
Feyzbakhsh, Soheyla
Pertusi, Laura
[J]. EPIJOURNAL DE GEOMETRIE ALGEBRIQUE, 2023, 7
[6] CUBIC FOURFOLDS WITH AN INVOLUTION
Marquand, Lisa
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2023, 376 (02) : 1373 - 1406
[7] On Ulrich bundles on projective bundles
Andreas Hochenegger
[J]. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2022, 63 : 573 - 587
[8] Planes in cubic fourfolds
Degtyarev, Alex
Itenberg, Ilia
Ottem, John Christian
[J]. ALGEBRAIC GEOMETRY, 2023, 10 (02): : 228 - 258
[9] On Ulrich bundles on projective bundles
Hochenegger, Andreas
[J]. BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY, 2022, 63 (03): : 573 - 587
[10] Some rational cubic fourfolds
Hassett, B
[J]. JOURNAL OF ALGEBRAIC GEOMETRY, 1999, 8 (01) : 103 - 114

← 1 2 3 4 5 →