Download this article
 Download this article For screen
For printing
Recent Issues

Volume 29
Issue 7, 3345–3919
Issue 6, 2783–3343
Issue 5, 2251–2782
Issue 4, 1693–2250
Issue 3, 1115–1691
Issue 2, 549–1114
Issue 1, 1–548

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
A tropical computation of refined toric invariants

Thomas Blomme

Geometry & Topology 29 (2025) 3129–3185
Bibliography
1 L Blechman, E Shustin, Refined descendant invariants of toric surfaces, Discrete Comput. Geom. 62 (2019) 180 MR3959926
2 F Block, L Göttsche, Refined curve counting with tropical geometry, Compos. Math. 152 (2016) 115 MR3453390
3 T Blomme, An imaginary refined count for some real rational curves, Beitr. Algebra Geom. 64 (2023) 721 MR4615493
4 T Blomme, A Caporaso–Harris type formula for relative refined invariants, Ann. Inst. Fourier (Grenoble) 75 (2025) 2101 MR4940721
5 P Bousseau, Tropical refined curve counting from higher genera and lambda classes, Invent. Math. 215 (2019) 1 MR3904449
6 K Conrad, A multivariable Hensel’s lemma, lecture note (2020)
7 J Forsgård, P Johansson, Coamoebas and line arrangements in dimension two, Math. Z. 278 (2014) 25 MR3267567
8 L Göttsche, F Schroeter, Refined broccoli invariants, J. Algebraic Geom. 28 (2019) 1 MR3875360
9 L Göttsche, V Shende, Refined curve counting on complex surfaces, Geom. Topol. 18 (2014) 2245 MR3268777
10 I Itenberg, G Mikhalkin, On Block–Göttsche multiplicities for planar tropical curves, Int. Math. Res. Not. 2013 (2013) 5289 MR3142257
11 G Mikhalkin, Enumerative tropical algebraic geometry in 2, J. Amer. Math. Soc. 18 (2005) 313 MR2137980
12 G Mikhalkin, Tropical geometry and its applications, from: "International Congress of Mathematicians, II" (editors M Sanz-Solé, J Soria, J L Varona, J Verdera), Eur. Math. Soc. (2006) 827 MR2275625
13 G Mikhalkin, Quantum indices and refined enumeration of real plane curves, Acta Math. 219 (2017) 135 MR3765660
14 J Nicaise, S Payne, F Schroeter, Tropical refined curve counting via motivic integration, Geom. Topol. 22 (2018) 3175 MR3858763
15 T Nishinou, B Siebert, Toric degenerations of toric varieties and tropical curves, Duke Math. J. 135 (2006) 1 MR2259922
16 F Schroeter, E Shustin, Refined elliptic tropical enumerative invariants, Israel J. Math. 225 (2018) 817 MR3805667
17 E Shustin, A tropical approach to enumerative geometry, Algebra i Analiz 17 (2005) 170 MR2159589
18 E Shustin, A tropical calculation of the Welschinger invariants of real toric del Pezzo surfaces, J. Algebraic Geom. 15 (2006) 285 MR2199066
19 I Tyomkin, Tropical geometry and correspondence theorems via toric stacks, Math. Ann. 353 (2012) 945 MR2923954
20 I Tyomkin, Enumeration of rational curves with cross-ratio constraints, Adv. Math. 305 (2017) 1356 MR3570161
21 J Y Welschinger, Invariants of real symplectic 4–manifolds and lower bounds in real enumerative geometry, Invent. Math. 162 (2005) 195 MR2198329