## Michigan Mathematical Journal

### On Gromov–Witten Theory of Projective Bundles

#### Article information

Source
Michigan Math. J., Volume 69, Issue 1 (2020), 153-178.

Dates
Revised: 17 August 2018
First available in Project Euclid: 14 November 2019

https://projecteuclid.org/euclid.mmj/1573700736

Digital Object Identifier
doi:10.1307/mmj/1573700736

Mathematical Reviews number (MathSciNet)
MR4071348

Zentralblatt MATH identifier
07208928

#### Citation

Fan, Honglu; Lee, Yuan-Pin. On Gromov–Witten Theory of Projective Bundles. Michigan Math. J. 69 (2020), no. 1, 153--178. doi:10.1307/mmj/1573700736. https://projecteuclid.org/euclid.mmj/1573700736

#### References

• [1] M. F. Atiyah and E. Rees, Vector bundles on projective 3-space, Invent. Math. 35 (1976), 131–153.
• [2] A. Biaĺynicki-Birula, Some theorems on actions of algebraic groups, Ann. of Math. (2) 98 (1973), 480–497.
• [3] J. Brown, Gromov–Witten Invariants of Toric Fibrations, arXiv:0901.1290version.
• [4] I. Ciocan-Fontanine and B. Kim, Wall-crossing in genus zero quasimap theory and mirror maps, Algebr. Geom. 1 (2014), no. 4, 400–448.
• [5] T. Coates, A. Corti, H. Iritani, and H. Tseng, Computing genus-zero twisted Gromov–Witten invariants, Duke Math. J. 147 (2009), no. 3, 377–438.
• [6] T. Coates, A. Givental, and H. Tseng, Virasoro constraints for toric bundles, arXiv:1508.06282.
• [7] A. Givental, Symplectic geometry of Frobenius structures, Frobenius manifolds, Aspects Math., E36, pp. 91–112, Friedr. Vieweg, Wiesbaden, 2004.
• [8] T. Graber and R. Pandharipande, Localization of virtual classes, Invent. Math. 135 (1999), no. 2, 487–518.
• [9] Y.-P. Lee, H.-W. Lin, F. Qu, and C.-L. Wang, Invariance of quantum rings under ordinary flops: III, arXiv:1401.7097.
• [10] Y.-P. Lee, H.-W. Lin, and C.-L. Wang, Invariance of Quantum Rings under Ordinary Flops I: Quantum corrections and reduction to local models, Algebr. Geom., to appear, arXiv:1109.5540.
• [11] Y.-P. Lee, H.-W. Lin, and C.-L. Wang, Invariance of Quantum Rings under Ordinary Flops II: a quantum Leray–Hirsch theorem, Algebr. Geom., to appear. arXiv:1311.5725.
• [12] Y.-P. Lee, H.-W. Lin, and C.-L. Wang, Birational Transformation and degeneration in Gromov–Witten theory, Reported by the first author in the AMS summer institute, July 2015.
• [13] Y.-P. Lee, H.-W. Lin, and C.-L. Wang, Quantum cohomology under birational maps and transitions, submitted to Proceedings of String-Math 2015 conference.
• [14] Y.-P. Lee and R. Pandharipande, Frobenius manifolds, Gromov–Witten theory, and Virasoro constraints, unfinished book available at https://www.math.utah.edu/~yplee/research/.
• [15] C.-C. M. Liu, Localization in Gromov–Witten theory and orbifold Gromov–Witten theory, Handbook of moduli. Vol. II, Adv. Lect. Math. (ALM), 25, pp. 353–425, Int. Press, Somerville, MA, 2013.
• [16] D. Maulik and R. Pandharipande, A topological view of Gromov–Witten theory, Topology 45 (2006), no. 5, 887–918.
• [17] A. Mustata and A. Mustata, Gromov–Witten invariants for varieties with $\mathbb{C}^{*}$ action, arXiv:1505.01471.
• [18] S. Payne, Moduli of toric vector bundles, Compos. Math. 144 (2008), no. 5, 1199–1213.
• [19] H. Sumihiro, Equivariant completion, J. Math. Kyoto Univ. 14 (1974), 1–28.