*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.