Bridgeland stability conditions and skew lines on ℙ ³

Inspired by Schmidt's work on twisted cubics, we study wall crossings in Bridgeland stability, starting with the Hilbert scheme Hilb2m+2(P3) parametrizing pairs of skew lines and plane conics union a point. We find two walls. Each wall crossing corresponds to a contraction of a divisor in the moduli space and the contracted space remains smooth. Building on work by Chen–Coskun–Nollet, we moreover prove that the contractions are K-negative extremal in the sense of Mori theory and so the moduli spaces are projective.