Revisiting the moduli space of 8 points on P1

Publikation: Arbeitspapier/Preprint › Preprint

Autoren

  • Klaus Hulek
  • Yota Maeda

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OriginalspracheEnglisch
PublikationsstatusElektronisch veröffentlicht (E-Pub) - 31 Okt. 2022

Abstract

The moduli space of \(8\) points on \(\mathbb{P}^1\), a so-called ancestral Deligne-Mostow space, is, by work of Kond\={o}, also a moduli space of K3 surfaces. We prove that the Deligne-Mostow isomorphism does not lift to a morphism between the Kirwan blow-up of the GIT quotient and the unique toroidal compactification of the corresponding ball quotient. Moreover, we show that these spaces are not \(K\)-equivalent, even though they are natural blow-ups at the unique cusps and have the same cohomology. This is analogous to the work of Casalaina-Martin-Grushevsky-Hulek-Laza on the moduli space of cubic surfaces. We further briefly discuss other cases of moduli space of points in \(\mathbb{P}^1\) where a similar behaviour can be observed, hinting at a more general, but not yet fully understood phenomenon. The moduli spaces of ordinary stable maps, that is the Fulton-MacPherson compactification of the configuration space of points in \(\mathbb{P}^1\), play an important role in the proof.

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Revisiting the moduli space of 8 points on P1. / Hulek, Klaus; Maeda, Yota.
2022.

Publikation: Arbeitspapier/Preprint › Preprint

Hulek, K., & Maeda, Y. (2022). Revisiting the moduli space of 8 points on P1. Vorabveröffentlichung online. https://doi.org/10.48550/arXiv.2211.00052
Hulek K, Maeda Y. Revisiting the moduli space of 8 points on P1. 2022 Okt 31. Epub 2022 Okt 31. doi: 10.48550/arXiv.2211.00052
Hulek, Klaus ; Maeda, Yota. / Revisiting the moduli space of 8 points on P1. 2022.
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