MIRROR SYMMETRY AND THE CLASSIFICATION OF ORBIFOLD DEL PEZZO SURFACES

被引:37
|
作者
Akhtar, Mohammad [1 ]
Coates, Tom [1 ]
Corti, Alessio [1 ]
Heuberger, Liana [2 ]
Kasprzyk, Alexander [1 ]
Oneto, Alessandro [3 ]
Petracci, Andrea [1 ]
Prince, Thomas [1 ]
Tveiten, Ketil [3 ]
机构
[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, 180 Queens Gate, London SW7 2AZ, England
[2] Inst Math Jussieu, F-75005 Paris, France
[3] Stockholm Univ, Dept Math, SE-10691 Stockholm, Sweden
基金
英国工程与自然科学研究理事会; 欧洲研究理事会;
关键词
TORUS ACTIONS; SINGULARITIES; DEFORMATIONS; VARIETIES; GEOMETRY;
D O I
10.1090/proc/12876
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We state a number of conjectures that together allow one to classify a broad class of del Pezzo surfaces with cyclic quotient singularities using mirror symmetry. We prove our conjectures in the simplest cases. The conjectures relate mutation-equivalence classes of Fano polygons with Q-Gorenstein deformation classes of del Pezzo surfaces.
引用
收藏
页码:513 / 527
页数:15
相关论文
共 50 条
  • [31] On the classification of Kahler-Ricci solitons on Gorenstein del Pezzo surfaces
    Cable, Jacob
    Suss, Hendrik
    EUROPEAN JOURNAL OF MATHEMATICS, 2018, 4 (01) : 137 - 161
  • [32] Classification of toric log del Pezzo surfaces with few singular points
    Suyama, Yusuke
    ELECTRONIC JOURNAL OF COMBINATORICS, 2021, 28 (01): : 1 - 17
  • [33] Webs of rational curves on real surfaces and a classification of real weak del Pezzo surfaces
    Lubbes, Niels
    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2021, 103 (02): : 398 - 448
  • [34] Elementary theory of Del Pezzo surfaces
    Schicho, J
    COMPUTATIONAL METHODS FOR ALGEBRAIC SPLINE SURFACES, 2005, : 77 - 94
  • [35] REGULAR DEL PEZZO SURFACES WITH IRREGULARITY
    Maddock, Zachary
    JOURNAL OF ALGEBRAIC GEOMETRY, 2016, 25 (03) : 401 - 429
  • [36] Interpolation problems: del Pezzo surfaces
    Landesman, Aaron
    Patel, Anand
    ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2019, 19 (04) : 1389 - 1428
  • [37] Quantum mirror map for del Pezzo geometries
    Furukawa, Tomohiro
    Moriyama, Sanefumi
    Sugimoto, Yuji
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2020, 53 (38)
  • [38] Del Pezzo Surfaces with Many Symmetries
    Cheltsov, Ivan
    Wilson, Andrew
    JOURNAL OF GEOMETRIC ANALYSIS, 2013, 23 (03) : 1257 - 1289
  • [39] Del Pezzo Surfaces with Many Symmetries
    Ivan Cheltsov
    Andrew Wilson
    Journal of Geometric Analysis, 2013, 23 : 1257 - 1289
  • [40] Del Pezzo surfaces with nonrational singularities
    I. A. Chel’tsov
    Mathematical Notes, 1997, 62 : 377 - 389