Geometry & Topology Volume 22, issue 6 (2018)

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Tropical refined curve counting via motivic integration

Johannes Nicaise, Sam Payne and Franziska Schroeter

Geometry & Topology 22 (2018) 3175–3234

DOI: 10.2140/gt.2018.22.3175

Bibliography

1	D Abramovich, L Caporaso, S Payne, The tropicalization of the moduli space of curves, Ann. Sci. Éc. Norm. Supér. 48 (2015) 765 MR3377065
2	M Baker, S Payne, J Rabinoff, Nonarchimedean geometry, tropicalization, and metrics on curves, Algebr. Geom. 3 (2016) 63 MR3455421
3	A Beauville, Counting rational curves on K3 surfaces, Duke Math. J. 97 (1999) 99 MR1682284
4	V G Berkovich, Étale cohomology for non–Archimedean analytic spaces, Inst. Hautes Études Sci. Publ. Math. 78 (1993) 5 MR1259429
5	V G Berkovich, Complex analytic vanishing cycles for formal schemes, preprint (2015)
6	V G Berkovich, Finiteness theorems for vanishing cycles of formal schemes, Israel J. Math. 210 (2015) 147 MR3430272
7	F Block, L Göttsche, Refined curve counting with tropical geometry, Compos. Math. 152 (2016) 115 MR3453390
8	L A Borisov, The class of the affine line is a zero divisor in the Grothendieck ring, J. Algebraic Geom. 27 (2018) 203 MR3764275
9	J Denef, F Loeser, Geometry on arc spaces of algebraic varieties, from: "European Congress of Mathematics, I" (editors C Casacuberta, R M Miró-Roig, J Verdera, S Xambó-Descamps), Progr. Math. 201, Birkhäuser (2001) 327 MR1905328
10	L van den Dries, o-minimal structures and real analytic geometry, from: "Current developments in mathematics, 1998" (editors B Mazur, W Schmid, S T Yau, D Jerison, I Singer, D Stroock), International (1999) 105 MR1772324
11	B Fantechi, L Göttsche, D van Straten, Euler number of the compactified Jacobian and multiplicity of rational curves, J. Algebraic Geom. 8 (1999) 115 MR1658220
12	S A Filippini, J Stoppa, Block–Göttsche invariants from wall-crossing, Compos. Math. 151 (2015) 1543 MR3383167
13	A Gathmann, H Markwig, Kontsevich’s formula and the WDVV equations in tropical geometry, Adv. Math. 217 (2008) 537 MR2370275
14	R Gopakumar, C Vafa, M–theory and topological strings, I, preprint (1998) arXiv:hep-th/9809187
15	R Gopakumar, C Vafa, M–theory and topological strings, II, preprint (1998) arXiv:hep-th/9812127
16	L Göttsche, V Shende, Refined curve counting on complex surfaces, Geom. Topol. 18 (2014) 2245 MR3268777
17	M Gross, Tropical geometry and mirror symmetry, 114, Amer. Math. Soc. (2011) MR2722115
18	A Grothendieck, Eléments de géométrie algébrique, IV : Étude locale des schémas et des morphismes de schémas, IV, Inst. Hautes Études Sci. Publ. Math. 32 (1967) 5 MR0238860
19	W Gubler, A guide to tropicalizations, from: "Algebraic and combinatorial aspects of tropical geometry" (editors E Brugallé, M A Cueto, A Dickenstein, E M Feichtner, I Itenberg), Contemp. Math. 589, Amer. Math. Soc. (2013) 125 MR3088913
20	J Harris, On the Severi problem, Invent. Math. 84 (1986) 445 MR837522
21	E Hrushovski, D Kazhdan, Integration in valued fields, from: "Algebraic geometry and number theory" (editor V Ginzburg), Progr. Math. 253, Birkhäuser (2006) 261 MR2263194
22	E Hrushovski, F Loeser, Monodromy and the Lefschetz fixed point formula, Ann. Sci. Éc. Norm. Supér. 48 (2015) 313 MR3346173
23	L Illusie, Théorie de Brauer et caractéristique d’Euler–Poincaré (d’après P Deligne), from: "The Euler–Poincaré characteristic", Astérisque 82, Soc. Math. France (1981) 161 MR629127
24	L Illusie, K Kato, C Nakayama, Quasi-unipotent logarithmic Riemann–Hilbert correspondences, J. Math. Sci. Univ. Tokyo 12 (2005) 1 MR2126784
25	I Itenberg, V Kharlamov, E Shustin, A Caporaso–Harris type formula for Welschinger invariants of real toric del Pezzo surfaces, Comment. Math. Helv. 84 (2009) 87 MR2466076
26	M Kapranov, The elliptic curve in the S–duality theory and Eisenstein series for Kac–Moody groups, preprint (2000) arXiv:math.AG/0001005
27	E Katz, Tropical realization spaces for polyhedral complexes, from: "Algebraic and combinatorial aspects of tropical geometry" (editors E Brugallé, M A Cueto, A Dickenstein, E M Feichtner, I Itenberg), Contemp. Math. 589, Amer. Math. Soc. (2013) 235 MR3088915
28	E Katz, S Payne, Realization spaces for tropical fans, from: "Combinatorial aspects of commutative algebra and algebraic geometry" (editors G Fløystad, T Johnsen, A L Knutsen), Abel Symp. 6, Springer (2011) 73 MR2810427
29	E Katz, A Stapledon, Tropical geometry and the motivic nearby fiber, Compos. Math. 148 (2012) 269 MR2881316
30	E Katz, A Stapledon, Tropical geometry, the motivic nearby fiber, and limit mixed Hodge numbers of hypersurfaces, Res. Math. Sci. 3 (2016) MR3508247
31	M Kool, V Shende, R P Thomas, A short proof of the Göttsche conjecture, Geom. Topol. 15 (2011) 397 MR2776848
32	M Luxton, Z Qu, Some results on tropical compactifications, Trans. Amer. Math. Soc. 363 (2011) 4853 MR2806694
33	F Martin, Cohomology of locally closed semi-algebraic subsets, Manuscripta Math. 144 (2014) 373 MR3227519
34	G Mikhalkin, Enumerative tropical algebraic geometry in ℝ², J. Amer. Math. Soc. 18 (2005) 313 MR2137980
35	G Mikhalkin, Quantum indices and refined enumeration of real plane curves, Acta Math. 219 (2017) 135 MR3765660
36	J Nicaise, Singular cohomology of the analytic Milnor fiber, and mixed Hodge structure on the nearby cohomology, J. Algebraic Geom. 20 (2011) 199 MR2762990
37	J Nicaise, J Sebag, Motivic Serre invariants, ramification, and the analytic Milnor fiber, Invent. Math. 168 (2007) 133 MR2285749
38	J Nicaise, J Sebag, The Grothendieck ring of varieties, from: "Motivic integration and its interactions with model theory and non-Archimedean geometry, I" (editors R Cluckers, J Nicaise, J Sebag), London Math. Soc. Lecture Note Ser. 383, Cambridge Univ. Press (2011) 145 MR2885336
39	T Nishinou, Correspondence theorems for tropical curves, I, preprint (2009) arXiv:0912.5090
40	T Nishinou, B Siebert, Toric degenerations of toric varieties and tropical curves, Duke Math. J. 135 (2006) 1 MR2259922
41	B Osserman, S Payne, Lifting tropical intersections, Doc. Math. 18 (2013) 121 MR3064984
42	R Pandharipande, R P Thomas, Stable pairs and BPS invariants, J. Amer. Math. Soc. 23 (2010) 267 MR2552254
43	A Robinson, Complete theories, North-Holland (1956) MR0075897
44	J P Serre, Représentations linéaires des groupes finis, Hermann (1967) MR0232867
45	A J Stewart, V Vologodsky, Motivic integral of K3 surfaces over a non-archimedean field, Adv. Math. 228 (2011) 2688 MR2838055
46	I Tyomkin, Tropical geometry and correspondence theorems via toric stacks, Math. Ann. 353 (2012) 945 MR2923954
47	S T Yau, E Zaslow, BPS states, string duality, and nodal curves on K3, Nuclear Phys. B 471 (1996) 503 MR1398633