Tropical discriminants

Journal of the American Mathematical Society

Volumn 20, Issue 4, 2007, Pages 1111-1133

  Dickenstein, Alicia ^a   Feichtner, Eva Maria ^b,c   Sturmfels, Bernd ^d  

^a UNIVERSIDAD DE BUENOS AIRES   (Argentina)

^b ETH ZURICH   (Switzerland)

^c UNIVERSITY OF STUTTGART   (Germany)

^d UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Discriminant; Dual variety; Tropical geometry

Indexed keywords

EID: 39549113966     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0894-0347-07-00562-0     Document Type: Article

References (24)

1. F. Ardila, C. Klivans: The Bergman complex of a matroid and phylogenetic trees; Journal of Combinatorial Theory Series B 96 (2006), 38-49. MR2185977 (2006i:05034) (Pubitemid 41823992)
2. R. Bieri, J. Groves: The geometry of the set of characters induced by valuations; Journal für die reine und angewandte Mathematik 347 (1984), 168-195. MR733052 (86c:14001)
3. T. Bogart, A. Jensen, D. Speyer, B. Sturmfels, R. Thomas: Computing tropical varieties; Journal of Symbolic Computation 42, Issue 1-2 (special issue on the occasion of MEGA 2005) (2007), 54-73. MR2284285
4. E. Cattani, A. Dickenstein, B. Sturmfels: Rational hypergeometric functions; Compositio Mathematica 128 (2001), 217-240. MR1850183 (2003f:33016)
5. C. De Concini, C. Procesi: Hyperplane arrangements and holonomy equations; Selecta Mathematica (N. S.) 1 (1995), 495-535. MR1366623 (97k:14014)
6. A. Dickenstein, B. Sturmfels: Elimination theory in codimension 2; Journal of Symbolic Computation 34 (2002), 119-135. MR1930829 (2003h:14073)
7. M. Einsiedler, M. Kapranov, D. Lind: Non-archimedean amoebas and tropical varieties; Journal für die reine und angewandte Mathematik 601 (2006), 139-157. MR2289207
8. E. M. Feichtner, D. Kozlov: Incidence combinatorics of resolutions; Selecta Mathematica (N. S.) 10 (2004), 37-60. MR2061222 (2006k:06008)
9. E. M. Feichtner, I. Müller: On the topology of nested set complexes; Proceedings of the American Mathematical Society 133 (2005), 999-1006. MR2117200 (2006c:06005)
10. E. M. Feichtner, B. Sturmfels: Matroid polytopes, nested sets and Bergman fans; Portugaliae Mathematica (N. S.) 62 (2005), 437-468. MR2191630 (2006j:05036)
11. E. M. Feichtner, S. Yuzvinsky: Chow rings of toric varieties defined by atomic lattices; Inventiones Mathematicae 155 (2004), 515-536. MR2038195 (2004k:14009)
12. A. Gathmann, H. Markwig: The numbers of tropical plane curves through points in general position; Journal für die reine und angewandte Mathematik, to appear, math. AG/0504390.
13. I. M. Gel'fand, M. M. Kapranov, A. V. Zelevinsky: Discriminants, Resultants, and Multidimensional Determinants; Birkhäuser, Boston, MA, 1994. MR1264417 (95e:14045)
14. J. P. Jouanolou: Ideaux Resultants; Advances in Mathematics 37 (1980), 212-238. MR591727 (82c:14038)
15. M. Kalkbrener, B. Sturmfels: Initial complexes of prime ideals; Advances in Mathematics 116 (1995), 365-376. MR1363769 (97g:13043)
16. M. Kapranov: A characterization of A-discriminantal hypersurfaces in terms of the logarithmic Gauss map; Mathematische Annalen 290 (1991), 277-285. MR1109634 (92j:14066)
17. E. Katz: The tropical degree of cones in the secondary fan, math. AG /0604290.
18. 2; Journal of the American Mathematical Society 18 (2005), 313-377. MR2137980 (2006b:14097)
19. J. Richter-Gebert, B. Sturmfels, T. Theobald: First steps in tropical geometry; in: "Idempotent Mathematics and Mathematical Physics, " Proceedings Vienna 2003 (G. L. Litvinov and V. P. Maslov, eds.), American Math. Society, Contemporary Mathematics 377 (2005), pp. 289-317. MR2149011 (2006d:14073)
20. D. Speyer: Tropical Geometry; Ph. D. Dissertation, University of California at Berkeley, 2005.
21. D. Speyer, B. Sturmfels: The tropical Grassmannian; Advances in Geometry 4 (2004), 389-411. MR2071813 (2005d:14089)
22. B. Sturmfels: On the Newton polytope of the resultant; Journal of Algebraic Combinatorics 3 (1994), 207-236. MR1268576 (95j:52024)
23. B. Sturmfels: Solving Systems of Polynomial Equations; CBMS Regional Conference Series in Mathematics 97, American Mathematical Society, Providence, 2002. MR1925796 (2003i:13037)
24. E. Tevelev: Compactifications of subvarieties of tori; American Journal of Mathematics, to appear, math. AG/0412329.