Geodesic
Staircase symmetries in Hirzebruch surfaces
Magill, Nicki1 ; McDuff, Dusa2
1 Mathematics Department, Cornell University, Ithaca, NY, United States
2 Mathematics Department, Barnard College, New York, NY, United States
Algebraic and Geometric Topology, Tome 23 (2023) no. 9, pp. 4235-4307

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

This paper continues the investigation of staircases in the family of Hirzebruch surfaces formed by blowing up the projective plane with weight b, that was started by Bertozzi, Holm Maw, McDuff, Mwakyoma, Pires and Weiler (2021). We explain the symmetries underlying the structure of the set of b that admit staircases, and show how the properties of these symmetries arise from a governing Diophantine equation. We also greatly simplify the techniques needed to show that a family of steps does form a staircase by using arithmetic properties of the accumulation function. There should be analogous results about both staircases and mutations for the other rational toric domains considered, for example, by Cristofaro-Gardiner, Holm, Mandini and Pires (2020) and by Casals and Vianna (2022).

DOI : 10.2140/agt.2023.23.4235
Keywords: symplectic embeddings in four dimensions, symplectic capacity function, Diophantine equation

Magill, Nicki 1 ; McDuff, Dusa 2

1 Mathematics Department, Cornell University, Ithaca, NY, United States
2 Mathematics Department, Barnard College, New York, NY, United States 
@article{10_2140_agt_2023_23_4235,
     author = {Magill, Nicki and McDuff, Dusa},
     title = {Staircase symmetries in {Hirzebruch} surfaces},
     journal = {Algebraic and Geometric Topology},
     pages = {4235--4307},
     publisher = {mathdoc},
     volume = {23},
     number = {9},
     year = {2023},
     doi = {10.2140/agt.2023.23.4235},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.4235/}
}
TY  - JOUR
AU  - Magill, Nicki
AU  - McDuff, Dusa
TI  - Staircase symmetries in Hirzebruch surfaces
JO  - Algebraic and Geometric Topology
PY  - 2023
SP  - 4235
EP  - 4307
VL  - 23
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.4235/
DO  - 10.2140/agt.2023.23.4235
ID  - 10_2140_agt_2023_23_4235
ER  - 
%0 Journal Article
%A Magill, Nicki
%A McDuff, Dusa
%T Staircase symmetries in Hirzebruch surfaces
%J Algebraic and Geometric Topology
%D 2023
%P 4235-4307
%V 23
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.4235/
%R 10.2140/agt.2023.23.4235
%F 10_2140_agt_2023_23_4235
Magill, Nicki; McDuff, Dusa. Staircase symmetries in Hirzebruch surfaces. Algebraic and Geometric Topology, Tome 23 (2023) no. 9, pp. 4235-4307. doi: 10.2140/agt.2023.23.4235

Cité par Sources :