2023/04/25 by Swinarski, David
#13A50 (Secondary) #14L24 (Primary) 14D22 #14Q05 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2304.12936
Mukai showed that the GIT quotient Gr(7,16) / / Spin(10) is a birational model of the moduli space of Deligne-Mumford stable genus 7 curves M7. The key observation is that a general smooth genus 7 curve can be realized as the intersection of the orthogonal Grassmannian OG(5,10) in ℙ15 with a six-dimensional projective linear subspace. What objects appear on the boundary of Mukai's model? As a first step in this study, computer calculations in Macaulay2, Magma, and Sage are used to find and analyze linear spaces yielding three examples of singular curves: a 7-cuspidal curve, the balanced ribbon of genus 7, and a family of genus 7 reducible nodal curves. Spin(10)-semistability is established by constructing and evaluating an invariant polynomial.