Abstract
We describe a compactification by KSBA stable pairs of the five-dimensional moduli space of K3 surfaces with a purely non-symplectic automorphism of order four and$U(2)\oplus D_4^{\oplus 2}$lattice polarization. These K3 surfaces can be realized as the minimal resolution of the double cover of$\mathbb {P}^{1}\times \mathbb {P}^{1}$branched along a specific$(4,\,4)$curve. We show that, up to a finite group action, this stable pairs compactification is isomorphic to Kirwan's partial desingularization of the GIT quotient$(\mathbb {P}^{1})^{8}{/\!/}\mathrm {SL}_2$with the symmetric linearization.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.