We perform a variation of geometric invariant theory stability analysis for 2nd Hilbert points of bi-log-canonically embedded pointed curves of genus . As a result, we give a GIT construction of the log canonical models for and obtain a VGIT presentation of the second flip in the Hassett–Keel program for the moduli space of pointed genus curves.
"VGIT Presentation of the Second Flip of ." Michigan Math. J. 69 (3) 487 - 514, August 2020. https://doi.org/10.1307/mmj/1596700815