Geometry & Topology Volume 28, issue 7 (2024)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Gromov–Witten theory via roots and logarithms

Luca Battistella, Navid Nabijou and Dhruv Ranganathan

Geometry & Topology 28 (2024) 3309–3355

DOI: 10.2140/gt.2024.28.3309

Bibliography

1	D Abramovich, Lectures on Gromov–Witten invariants of orbifolds, from: "Enumerative invariants in algebraic geometry and string theory" (editors K Behrend, M Manetti), Lecture Notes in Math. 1947, Springer (2008) 1 MR2493583
2	D Abramovich, Q Chen, Stable logarithmic maps to Deligne–Faltings pairs, II, Asian J. Math. 18 (2014) 465 MR3257836
3	D Abramovich, K Karu, Weak semistable reduction in characteristic 0, Invent. Math. 139 (2000) 241 MR1738451
4	D Abramovich, A Vistoli, Compactifying the space of stable maps, J. Amer. Math. Soc. 15 (2002) 27 MR1862797
5	D Abramovich, T Graber, A Vistoli, Gromov–Witten theory of Deligne–Mumford stacks, Amer. J. Math. 130 (2008) 1337 MR2450211
6	D Abramovich, M Olsson, A Vistoli, Twisted stable maps to tame Artin stacks, J. Algebraic Geom. 20 (2011) 399 MR2786662
7	D Abramovich, S Marcus, J Wise, Comparison theorems for Gromov–Witten invariants of smooth pairs and of degenerations, Ann. Inst. Fourier (Grenoble) 64 (2014) 1611 MR3329675
8	D Abramovich, Q Chen, S Marcus, M Ulirsch, J Wise, Skeletons and fans of logarithmic structures, from: "Nonarchimedean and tropical geometry" (editors M Baker, S Payne), Springer (2016) 287 MR3702314
9	D Abramovich, C Cadman, J Wise, Relative and orbifold Gromov–Witten invariants, Algebr. Geom. 4 (2017) 472 MR3683504
10	D Abramovich, Q Chen, M Gross, B Siebert, Punctured logarithmic maps, preprint (2020) arXiv:2009.07720
11	E Andreini, Y Jiang, H H Tseng, Gromov–Witten theory of root gerbes, I : Structure of genus 0 moduli spaces, J. Differential Geom. 99 (2015) 1 MR3299821
12	E Andreini, Y Jiang, H H Tseng, Gromov–Witten theory of product stacks, Comm. Anal. Geom. 24 (2016) 223 MR3514559
13	H Argüz, M Gross, The higher-dimensional tropical vertex, Geom. Topol. 26 (2022) 2135 MR4520304
14	Y Bae, J Schmitt, Chow rings of stacks of prestable curves, I, Forum Math. Sigma 10 (2022) MR4430955
15	L Battistella, N Nabijou, Relative quasimaps and mirror formulae, Int. Math. Res. Not. 2021 (2021) 7885 MR4259162
16	L Battistella, N Nabijou, H H Tseng, F You, The local-orbifold correspondence for simple normal crossing pairs, J. Inst. Math. Jussieu 22 (2023) 2515 MR4624970
17	K Behrend, The product formula for Gromov–Witten invariants, J. Algebraic Geom. 8 (1999) 529 MR1689355
18	A M Botero, Intersection theory of toric b–divisors in toric varieties, J. Algebraic Geom. 28 (2019) 291 MR3912060
19	J Brown, Gromov–Witten invariants of toric fibrations, Int. Math. Res. Not. 2014 (2014) 5437 MR3267376
20	C Cadman, Using stacks to impose tangency conditions on curves, Amer. J. Math. 129 (2007) 405 MR2306040
21	C Cadman, L Chen, Enumeration of rational plane curves tangent to a smooth cubic, Adv. Math. 219 (2008) 316 MR2435425
22	F Carocci, N Nabijou, Tropical expansions and toric variety bundles, preprint (2022) arXiv:2207.12541
23	F Carocci, N Nabijou, Rubber tori in the boundary of expanded stable maps, J. Lond. Math. Soc. 109 (2024)
24	R Cavalieri, M Chan, M Ulirsch, J Wise, A moduli stack of tropical curves, Forum Math. Sigma 8 (2020) MR4091085
25	Q Chen, Stable logarithmic maps to Deligne–Faltings pairs, I, Ann. of Math. 180 (2014) 455 MR3224717
26	B Chen, C Y Du, R Wang, Orbifold Gromov–Witten theory of weighted blowups, Sci. China Math. 63 (2020) 2475 MR4182136
27	D Cheong, I Ciocan-Fontanine, B Kim, Orbifold quasimap theory, Math. Ann. 363 (2015) 777 MR3412343
28	T Coates, A Gholampour, H Iritani, Y Jiang, P Johnson, C Manolache, The quantum Lefschetz hyperplane principle can fail for positive orbifold hypersurfaces, Math. Res. Lett. 19 (2012) 997 MR3039825
29	K Costello, Higher genus Gromov–Witten invariants as genus zero invariants of symmetric products, Ann. of Math. 164 (2006) 561 MR2247968
30	D A Cox, J B Little, H K Schenck, Toric varieties, 124, Amer. Math. Soc. (2011) MR2810322
31	H Fan, Chern classes and Gromov–Witten theory of projective bundles, Amer. J. Math. 143 (2021) 811 MR4270258
32	H Fan, L Wu, F You, Structures in genus-zero relative Gromov–Witten theory, J. Topol. 13 (2020) 269 MR4138739
33	H Fan, L Wu, F You, Higher genus relative Gromov–Witten theory and double ramification cycles, J. Lond. Math. Soc. 103 (2021) 1547 MR4273479
34	A Gathmann, Absolute and relative Gromov–Witten invariants of very ample hypersurfaces, Duke Math. J. 115 (2002) 171 MR1944571
35	A Gathmann, Gromov–Witten invariants of hypersurfaces, Habilitationsschrift, Universität Kaiserslautern (2003)
36	M Gross, B Siebert, Logarithmic Gromov–Witten invariants, J. Amer. Math. Soc. 26 (2013) 451 MR3011419
37	M Gross, B Siebert, Intrinsic mirror symmetry, preprint (2019) arXiv:1909.07649
38	M Gross, R Pandharipande, B Siebert, The tropical vertex, Duke Math. J. 153 (2010) 297 MR2667135
39	L Herr, J Wise, Costello’s pushforward formula : errata and generalization, Manuscripta Math. 171 (2023) 621 MR4597710
40	D Holmes, R Schwarz, Logarithmic intersections of double ramification cycles, Algebr. Geom. 9 (2022) 574 MR4490707
41	D Holmes, A Pixton, J Schmitt, Multiplicativity of the double ramification cycle, Doc. Math. 24 (2019) 545 MR3960120
42	F Janda, R Pandharipande, A Pixton, D Zvonkine, Double ramification cycles on the moduli spaces of curves, Publ. Math. Inst. Hautes Études Sci. 125 (2017) 221 MR3668650
43	F Janda, R Pandharipande, A Pixton, D Zvonkine, Double ramification cycles with target varieties, J. Topol. 13 (2020) 1725 MR4186143
44	K Kato, Toric singularities, Amer. J. Math. 116 (1994) 1073 MR1296725
45	F Kato, Log smooth deformation and moduli of log smooth curves, Int. J. Math. 11 (2000) 215 MR1754621
46	G Kempf, F F Knudsen, D Mumford, B Saint-Donat, Toroidal embeddings, I, 339, Springer (1973) MR0335518
47	P Kennedy-Hunt, N Nabijou, Q Shafi, W Zheng, Divisors and curves on logarithmic mapping spaces, preprint (2022) arXiv:2209.00630
48	B Kim, Logarithmic stable maps, from: "New developments in algebraic geometry, integrable systems and mirror symmetry" (editors M H Saito, S Hosono, K Yoshioka), Adv. Stud. Pure Math. 59, Math. Soc. Japan (2010) 167 MR2683209
49	A Kresch, Cycle groups for Artin stacks, Invent. Math. 138 (1999) 495 MR1719823
50	J Li, Stable morphisms to singular schemes and relative stable morphisms, J. Differential Geom. 57 (2001) 509 MR1882667
51	J Li, A degeneration formula of GW-invariants, J. Differential Geom. 60 (2002) 199 MR1938113
52	C C M Liu, Localization in Gromov–Witten theory and orbifold Gromov–Witten theory, from: "Handbook of moduli, II" (editors G Farkas, I Morrison), Adv. Lect. Math. 25, International (2013) 353 MR3184181
53	D Maclagan, B Sturmfels, Introduction to tropical geometry, 161, Amer. Math. Soc. (2015) MR3287221
54	T Mandel, H Ruddat, Descendant log Gromov–Witten invariants for toric varieties and tropical curves, Trans. Amer. Math. Soc. 373 (2020) 1109 MR4068259
55	C Manolache, Virtual pull-backs, J. Algebraic Geom. 21 (2012) 201 MR2877433
56	S Molcho, Universal stacky semistable reduction, Israel J. Math. 242 (2021) 55 MR4282076
57	S Molcho, D Ranganathan, A case study of intersections on blowups of the moduli of curves, Algebra Number Theory 18 (2024) 1767 MR4810072
58	N Nabijou, Recursion formulae in logarithmic Gromov–Witten theory and quasimap theory, PhD thesis, Imperial College London (2018)
59	N Nabijou, D Ranganathan, Gromov–Witten theory with maximal contacts, Forum Math. Sigma 10 (2022) MR4371043
60	T Nishinou, B Siebert, Toric degenerations of toric varieties and tropical curves, Duke Math. J. 135 (2006) 1 MR2259922
61	M C Olsson, (Log) twisted curves, Compos. Math. 143 (2007) 476 MR2309994
62	D Ranganathan, Skeletons of stable maps, I : Rational curves in toric varieties, J. Lond. Math. Soc. 95 (2017) 804 MR3664519
63	D Ranganathan, A note on the cycle of curves in a product of pairs, preprint (2019) arXiv:1910.00239
64	D Ranganathan, Logarithmic Gromov–Witten theory with expansions, Algebr. Geom. 9 (2022) 714 MR4518245
65	D Ranganathan, K Santos-Parker, J Wise, Moduli of stable maps in genus one and logarithmic geometry, I, Geom. Topol. 23 (2019) 3315 MR4046967
66	Q Shafi, Logarithmic quasimaps, Adv. Math. 438 (2024) 109469 MR4686744
67	H H Tseng, F You, On orbifold Gromov–Witten theory in codimension one, J. Pure Appl. Algebra 220 (2016) 3567 MR3497977
68	H H Tseng, F You, Higher genus relative and orbifold Gromov–Witten invariants, Geom. Topol. 24 (2020) 2749 MR4194303
69	H H Tseng, F You, A Gromov–Witten theory for simple normal-crossing pairs without log geometry, Comm. Math. Phys. 401 (2023) 803 MR4604908
70	H H Tseng, F You, A mirror theorem for multi-root stacks and applications, Selecta Math. 29 (2023) 6 MR4505176
71	J Wise, Uniqueness of minimal morphisms of logarithmic schemes, Algebr. Geom. 6 (2019) 50 MR3904798
72	Y Wu, Splitting of Gromov–Witten invariants with toric gluing strata, J. Algebraic Geom. 33 (2024) 213
73	F You, Relative quantum cohomology under birational transformations, preprint (2022) arXiv:2204.00509