Expansions for Hilbert Schemes: References

Table of Links

• Abstract and Intro
• Background on tropical perspective
• The expanded construction
• GIT stability
• Stack perspective
• The canonical moduli stack
• References

References

[AK16] Jarod Alper and Andrew Kresch. “Equivariant versal deformations of semistable curves”. In: Michigan Math. J. 65.2 (2016), pp. 227–250.

[EH00] David Eisenbud and Joe Harris. The geometry of schemes. Vol. 197. Graduate Texts in Mathematics. Springer-Verlag, New York, 2000, pp. x+294.

[FKX17] Tommaso de Fernex, J´anos Koll´ar, and Chenyang Xu. “The dual complex of singularities”. In: Higher dimensional algebraic geometry—in honour of Professor Yujiro Kawamata’s sixtieth birthday. Vol. 74. Adv. Stud. Pure Math. Math. Soc. Japan, Tokyo, 2017, pp. 103–129.

[GHH15] Martin G. Gulbrandsen, Lars H. Halle, and Klaus Hulek. “A relative HilbertMumford criterion”. In: Manuscripta Math. 148.3-4 (2015), pp. 283–301.

[GHH19] Martin G. Gulbrandsen, Lars H. Halle, and Klaus Hulek. “A GIT construction of degenerations of Hilbert schemes of points”. In: Doc. Math. 24 (2019), pp. 421–472.

[Ken23] Patrick Kennedy-Hunt. The Logarithmic Quot space: foundations and tropicalisation. 2023. arXiv: 2308.14470 [math.AG].

[KLSV18] J´anos Koll´ar, Radu Laza, Giulia Sacc`a, and Claire Voisin. “Remarks on degenerations of hyper-K¨ahler manifolds”. In: Ann. Inst. Fourier (Grenoble) 68.7 (2018), pp. 2837–2882.

[Li13] Jun Li. “Good degenerations of moduli spaces”. In: Handbook of moduli. Vol. II. Vol. 25. Adv. Lect. Math. (ALM). Int. Press, Somerville, MA, 2013, pp. 299–351.

[Log] Dan Abramovich, Qile Chen, Danny Gillam, Yuhao Huang, Martin Olsson, Matthew Satriano, and Shenghao Sun. “Logarithmic geometry and moduli”. In: Handbook of moduli. Vol. I. Vol. 24. Adv. Lect. Math. (ALM). Int. Press, Somerville, MA, 2013, pp. 1–61.

[LW15] Jun Li and Baosen Wu. “Good degeneration of Quot-schemes and coherent systems”. In: Comm. Anal. Geom. 23.4 (2015), pp. 841–921.

[MFK94] David Mumford, John Fogarty, and Frances Kirwan. Geometric invariant theory. Vol. 34. Ergebnisse der Mathematik und ihrer Grenzgebiete (2). Berlin: Springer Berlin, Heidelberg, 1994.

[MR20] Davesh Maulik and Dhruv Ranganathan. Logarithmic Donaldson–Thomas theory. 2020. url: arXiv:2006.06603v2.

[Nag08] Yasunari Nagai. “On monodromies of a degeneration of irreducible symplectic K¨ahler manifolds”. In: Math. Z. 258.2 (2008), pp. 407–426.

[Ran22a] Dhruv Ranganathan. “Logarithmic and tropical moduli theory”. Notes for GAeL lecture course. June 2022. url: https://www.dpmms.cam.ac.uk/~dr508/GAeL2022.p

[Ran22b] Dhruv Ranganathan. “Logarithmic Gromov-Witten theory with expansions”. In: Algebr. Geom. 9.6 (2022), pp. 714–761. 4

[Tev07] Jenia Tevelev. “Compactifications of subvarieties of tori”. In: Amer. J. Math. 129.4 (2007), pp. 1087–1104.