Geodesic
Phase tropical hypersurfaces
Kerr, Gabriel1 ; Zharkov, Ilia2
1 Department of Mathematics, Kansas State University, Manhattan, KS, United States
2 Mathematics Department, Kansas State University, Manhattan, KS, United States
Geometry & topology, Tome 22 (2018) no. 6, pp. 3287-3320.

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

We prove a conjecture of Viro (Tr. Mat. Inst. Steklova 273 (2011) 271–303) that a smooth complex hypersurface in (ℂ∗)n is homeomorphic to the corresponding phase tropical hypersurface.

DOI : 10.2140/gt.2018.22.3287
Classification : 14T05, 14J33
Keywords: phase tropical, hypersurface, tropical geometry

Kerr, Gabriel 1 ; Zharkov, Ilia 2

1 Department of Mathematics, Kansas State University, Manhattan, KS, United States
2 Mathematics Department, Kansas State University, Manhattan, KS, United States 
@article{GT_2018_22_6_a3,
     author = {Kerr, Gabriel and Zharkov, Ilia},
     title = {Phase tropical hypersurfaces},
     journal = {Geometry & topology},
     pages = {3287--3320},
     publisher = {mathdoc},
     volume = {22},
     number = {6},
     year = {2018},
     doi = {10.2140/gt.2018.22.3287},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/gt.2018.22.3287/}
}
TY  - JOUR
AU  - Kerr, Gabriel
AU  - Zharkov, Ilia
TI  - Phase tropical hypersurfaces
JO  - Geometry & topology
PY  - 2018
SP  - 3287
EP  - 3320
VL  - 22
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2140/gt.2018.22.3287/
DO  - 10.2140/gt.2018.22.3287
ID  - GT_2018_22_6_a3
ER  - 
%0 Journal Article
%A Kerr, Gabriel
%A Zharkov, Ilia
%T Phase tropical hypersurfaces
%J Geometry & topology
%D 2018
%P 3287-3320
%V 22
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2140/gt.2018.22.3287/
%R 10.2140/gt.2018.22.3287
%F GT_2018_22_6_a3
Kerr, Gabriel; Zharkov, Ilia. Phase tropical hypersurfaces. Geometry & topology, Tome 22 (2018) no. 6, pp. 3287-3320. doi : 10.2140/gt.2018.22.3287. http://geodesic.mathdoc.fr/articles/10.2140/gt.2018.22.3287/

[1] A Björner, Posets, regular CW complexes and Bruhat order, European J. Combin. 5 (1984) 7 | DOI

[2] R Forman, Morse theory for cell complexes, Adv. Math. 134 (1998) 90 | DOI

[3] I M Gel’Fand, M M Kapranov, A V Zelevinsky, Discriminants, resultants, and multidimensional determinants, Birkhäuser (1994) | DOI

[4] B Grünbaum, V P Sreedharan, An enumeration of simplicial 4–polytopes with 8 vertices, J. Combinatorial Theory 2 (1967) 437 | DOI

[5] Y R Kim, M Nisse, Geometry and a natural symplectic structure of phase tropical hypersurfaces, preprint (2016)

[6] R C Kirby, L C Siebenmann, Foundational essays on topological manifolds, smoothings, and triangulations, 88, Princeton Univ. Press (1977)

[7] A T Lundell, S Weingram, The topology of CW complexes, Van Nostrand (1969) | DOI

[8] D Maclagan, B Sturmfels, Introduction to tropical geometry, 161, Amer. Math. Soc. (2015)

[9] G Mikhalkin, Decomposition into pairs-of-pants for complex algebraic hypersurfaces, Topology 43 (2004) 1035 | DOI

[10] M Nisse, F Sottile, Non-Archimedean coamoebae, from: "Tropical and non-Archimedean geometry" (editors O Amini, M Baker, X Faber), Contemp. Math. 605, Amer. Math. Soc. (2013) 73 | DOI

[11] N Sheridan, On the homological mirror symmetry conjecture for pairs of pants, J. Differential Geom. 89 (2011) 271 | DOI

[12] O Viro, Gluing algebraic hypersurfaces, removing of singularities and constructions of curves, from: "Tezisy Leningradskoj mezhdunarodnoj topologicheskoj konferencii" (1983) 149

[13] O Y Viro, On basic concepts of tropical geometry, Tr. Mat. Inst. Steklova 273 (2011) 271 | DOI

Cité par Sources :