Cox rings of cubic surfaces and Fano threefolds

被引：8
|
作者：
Derenthal, Ulrich [2 ]
Hausen, Juergen [3 ]
Heim, Armand [3 ]
Keicher, Simon [3 ]
Laface, Antonio [1 ,4 ]
机构：
[1] Univ Concepcion, Dept Matemat, Concepcion, Chile
[2] Leibniz Univ Hannover, Inst Algebra Zahlentheorie & Diskrete Math, D-30167 Hannover, Germany
[3] Univ Tubingen, Math Inst, D-72076 Tubingen, Germany
[4] Univ Concepcion, Dept Matemat, Concepcion, Chile
来源：
JOURNAL OF ALGEBRA | 2015年 / 436卷
关键词：
Cox rings; Cubic surfaces; Fano varieties; DEL PEZZO SURFACES; RATIONAL-POINTS; MANINS CONJECTURE; BOUNDED HEIGHT; UNIVERSAL TORSORS; NUMBER; CLASSIFICATION;
D O I：
10.1016/j.jalgebra.2015.04.028
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We determine the Cox rings of the minimal resolutions of cubic surfaces with at most rational double points, of blow-ups of the projective plane at non-general configurations of six points and of three dimensional smooth Fano varieties of Picard numbers one and two. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码：228 / 276
页数：49
相关论文
共 50 条
  • [1] Singularities of Cox rings of Fano varieties
    Brown, Morgan
    JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2013, 99 (06): : 655 - 667
  • [2] Cox rings of degree one del Pezzo surfaces
    Testa, Damiano
    Varilly-Alvarado, Anthony
    Velasco, Mauricio
    ALGEBRA & NUMBER THEORY, 2009, 3 (07) : 729 - 761
  • [3] Cox rings over nonclosed fields
    Derenthal, Ulrich
    Pieropan, Marta
    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2019, 99 (02): : 447 - 476
  • [4] Quadratic congruences on average and rational points on cubic surfaces
    Baier, Stephan
    Derenthal, Ulrich
    ACTA ARITHMETICA, 2015, 171 (02) : 145 - 171
  • [5] COX RINGS OF EXTREMAL RATIONAL ELLIPTIC SURFACES
    Artebani, Michela
    Garbagnati, Alice
    Laface, Antonio
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 368 (03) : 1735 - 1757
  • [6] The maximal unipotent finite quotient, unusual torsion in Fano threefolds, and exceptional Enriques surfaces
    Fanelli, Andrea
    Schroeer, Stefan
    EPIJOURNAL DE GEOMETRIE ALGEBRIQUE, 2020, 4
  • [7] Gorensteinness and iteration of Cox rings for Fano type varieties
    Braun, Lukas
    MATHEMATISCHE ZEITSCHRIFT, 2022, 301 (01) : 1047 - 1061
  • [8] Gorensteinness and iteration of Cox rings for Fano type varieties
    Lukas Braun
    Mathematische Zeitschrift, 2022, 301 : 1047 - 1061
  • [9] On the rationality of Fano-Enriques threefolds
    Sarikyan, Arman
    ALGEBRAIC GEOMETRY, 2023, 10 (06): : 643 - 665
  • [10] ON THE EXTENDABILITY OF PROJECTIVE SURFACES AND A GENUS BOUND FOR ENRIQUES-FANO THREEFOLDS
    Knutsen, Andreas Leopold
    Lopez, Angelo Felice
    Munoz, Roberto
    JOURNAL OF DIFFERENTIAL GEOMETRY, 2011, 88 (03) : 483 - 518
12345