Geometry & Topology Volume 24, issue 6 (2020)

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Higher genus relative and orbifold Gromov–Witten invariants

Hsian-Hua Tseng and Fenglong You

Geometry & Topology 24 (2020) 2749–2779

DOI: 10.2140/gt.2020.24.2749

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, C Cadman, J Wise, Relative and orbifold Gromov–Witten invariants, Algebr. Geom. 4 (2017) 472 MR3683504
3	D Abramovich, B Fantechi, Orbifold techniques in degeneration formulas, Ann. Sc. Norm. Super. Pisa Cl. Sci. 16 (2016) 519 MR3559610
4	D Abramovich, T Graber, A Vistoli, Algebraic orbifold quantum products, from: "Orbifolds in mathematics and physics" (editors A Adem, J Morava, Y Ruan), Contemp. Math. 310, Amer. Math. Soc. (2002) 1 MR1950940
5	D Abramovich, T Graber, A Vistoli, Gromov–Witten theory of Deligne–Mumford stacks, Amer. J. Math. 130 (2008) 1337 MR2450211
6	C Cadman, Using stacks to impose tangency conditions on curves, Amer. J. Math. 129 (2007) 405 MR2306040
7	C Cadman, L Chen, Enumeration of rational plane curves tangent to a smooth cubic, Adv. Math. 219 (2008) 316 MR2435425
8	B Chen, C Y Du, R Wang, Orbifold Gromov–Witten theory of weighted blowups, preprint (2017)
9	W Chen, Y Ruan, Orbifold Gromov–Witten theory, from: "Orbifolds in mathematics and physics" (editors A Adem, J Morava, Y Ruan), Contemp. Math. 310, Amer. Math. Soc. (2002) 25 MR1950941
10	P Dunin-Barkowski, N Orantin, S Shadrin, L Spitz, Identification of the Givental formula with the spectral curve topological recursion procedure, Comm. Math. Phys. 328 (2014) 669 MR3199996
11	H Fan, L Wu, F You, Higher genus relative Gromov–Witten theory and DR–cycles, preprint (2019) arXiv:1907.07133
12	H Fan, L Wu, F You, Structures in genus-zero relative Gromov–Witten theory, J. Topol. 13 (2020) 269
13	A Geraschenko, M Satriano, A “bottom up” characterization of smooth Deligne–Mumford stacks, Int. Math. Res. Not. 2017 (2017) 6469 MR3719470
14	T Graber, R Pandharipande, Localization of virtual classes, Invent. Math. 135 (1999) 487 MR1666787
15	T Graber, R Vakil, Relative virtual localization and vanishing of tautological classes on moduli spaces of curves, Duke Math. J. 130 (2005) 1 MR2176546
16	E N Ionel, T H Parker, Relative Gromov–Witten invariants, Ann. of Math. 157 (2003) 45 MR1954264
17	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
18	F Janda, R Pandharipande, A Pixton, D Zvonkine, Double ramification cycles with target varieties, preprint (2018) arXiv:1812.10136
19	P D Johnson, Equivariant Gromov–Witten theory of one dimensional stacks, PhD thesis, University of Michigan (2009)
20	P Johnson, R Pandharipande, H H Tseng, Abelian Hurwitz–Hodge integrals, Michigan Math. J. 60 (2011) 171 MR2785870
21	A M Li, Y Ruan, Symplectic surgery and Gromov–Witten invariants of Calabi–Yau 3–folds, Invent. Math. 145 (2001) 151 MR1839289
22	J Li, A degeneration formula of GW–invariants, J. Differential Geom. 60 (2002) 199 MR1938113
23	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
24	C C M Liu, K Liu, J Zhou, A formula of two-partition Hodge integrals, J. Amer. Math. Soc. 20 (2007) 149 MR2257399
25	D Maulik, R Pandharipande, A topological view of Gromov–Witten theory, Topology 45 (2006) 887 MR2248516
26	S Molcho, E Routis, Localization for logarithmic stable maps, Trans. Amer. Math. Soc. Ser. B 6 (2019) 80 MR3905962
27	P Norbury, N Scott, Gromov–Witten invariants of ℙ¹ and Eynard–Orantin invariants, Geom. Topol. 18 (2014) 1865 MR3268770
28	A Okounkov, R Pandharipande, The equivariant Gromov–Witten theory of ℙ¹, Ann. of Math. 163 (2006) 561 MR2199226
29	A Okounkov, R Pandharipande, Gromov–Witten theory, Hurwitz theory, and completed cycles, Ann. of Math. 163 (2006) 517 MR2199225
30	A Okounkov, R Pandharipande, Virasoro constraints for target curves, Invent. Math. 163 (2006) 47 MR2208418
31	A Okounkov, R Pandharipande, Gromov–Witten theory, Hurwitz numbers, and matrix models, from: "Algebraic geometry, I" (editors D Abramovich, A Bertram, L Katzarkov, R Pandharipande, M Thaddeus), Proc. Sympos. Pure Math. 80, Amer. Math. Soc. (2009) 325 MR2483941
32	H H Tseng, Orbifold quantum Riemann–Roch, Lefschetz and Serre, Geom. Topol. 14 (2010) 1 MR2578300
33	H H Tseng, F You, Double ramification cycles on the moduli spaces of admissible covers, preprint (2016) arXiv:1606.03770
34	H H Tseng, F You, On orbifold Gromov–Witten theory in codimension one, J. Pure Appl. Algebra 220 (2016) 3567 MR3497977