Computing the Chow variety of quadratic space curves

Peter Bürgisser (1) , Kathlén Kohn (1) , Pierre Lairez (1) , Bernd Sturmfels (2)

1 Institut für Mathematik [Berlin]
2 Department of Mathematics [Berkeley]

Quadrics in the Grassmannian of lines in 3-space form a 19-dimensional projective space. We study the subvariety of coisotropic hypersurfaces. Following Gel'fand, Kapranov and Zelevinsky, it decomposes into Chow forms of plane conics, Chow forms of pairs of lines, and Hurwitz forms of quadric surfaces. We compute the ideals of these loci.

Mots clés: chow variety; parametrization; space curve; computation

Domaines: Géométrie algébrique [math.AG]; Calcul formel [cs.SC]

Peter Bürgisser, Kathlén Kohn, Pierre Lairez, Bernd Sturmfels. Computing the Chow variety of quadratic space curves. 2015. ⟨hal-01188213v1⟩