  In the previous paper, we construct new subvarieties in the varieties of
power sums for certain quartic hypersurfaces. In this paper, we show that these
quartics coincide with the Scorza quartics of general pairs of trigonal curves
and ineffective theta characteristics. Among other applications, we give an
affirmative answer to the conjecture of Dolgachev and Kanev on the existence of
the Scorza quartics for any general pairs of curves and ineffective theta
characteristics. We also give descriptions of the moduli spaces of trigonal
even spin curves. For curves of genus 4, we deepen this description in the next
paper.

Algebraic Geometry