The dimension of determinantal surfaces in projective 3-space

event Friday, March 31, 2023
access_time 3:45pm (CDT)
room PHSC 1105
free_breakfast Tea at 3:15pm (CDT) in PHSC 424

Abstract: A hypersurface X = {F = 0} in projective 3-space is called determinantal if there is an n×n matrix S, with homogeneous polynomial entries, such that F = det(S). Classically, a determinantal expression for a hypersurface X was studied because it provides interesting maps from X to projective space. For example, if a cubic surface is determinantal, then it follows that it is rational. Thus, in studying hypersurfaces one arrives at the question: what is the dimension of the family of determinantal hypersurfaces of degree d in projective 3-space? The main goal of this talk is to answer the previous question. This computation will exhibit that determinantal surfaces of degree 4 form a divisor with 5 irreducible components in the space of quartic surfaces. If time permits, I will compute that the degree of each of those components is 320, 2508, 136512, 38475, 320112.

For more information on this event, please contact Travis Mandel.