14 research outputs found
Geometric invariant theory of syzygies, with applications to moduli spaces
We define syzygy points of projective schemes, and introduce a program of
studying their GIT stability. Then we describe two cases where we have managed
to make some progress in this program, that of polarized K3 surfaces of odd
genus, and of genus six canonical curves. Applications of our results include
effectivity statements for divisor classes on the moduli space of odd genus K3
surfaces, and a new construction in the Hassett-Keel program for the moduli
space of genus six curves.Comment: v1: 23 pages, submitted to the Proceedings of the Abel Symposium
2017, v2: final version, corrects a sign error and resulting divisor class
calculations on the moduli space of K3 surfaces in Section 5, other minor
changes, In: Christophersen J., Ranestad K. (eds) Geometry of Moduli.
Abelsymposium 2017. Abel Symposia, vol 14. Springer, Cha
Brill–Noether general K3 surfaces with the maximal number of elliptic pencils of minimal degree
We explicitly construct Brill–Noether general K3 surfaces of genus 4, 6 and 8 having the maximal number of elliptic pencils of degrees 3, 4 and 5, respectively, and study their moduli spaces and moduli maps to the moduli space of curves. As an application we prove the existence of Brill–Noether general K3 surfaces of genus 4 and 6 without stable Lazarsfeld–Mukai bundles of minimal c2.publishedVersio