About the College
Geometry and Physics Seminar: On Real Determinantal Quartics
February 10 at 4:00 PM to 5:00 PMUngar Room 402
Mathematics Lecture
Professor I. Itenberg
Université de Strasbourg
will present
On Real Determinantal Quartics
Wednesday, February 10, 2010, 4:00pm
Ungar Room 402
Abstract: Let A_0, A_1, A_2, and A_3 be real symmetric 4 x 4 matrices. One can associate to these four matrices a spectral surface in the three dimensional complex projective space CP^3 (the set of points (x_0 : x_1 : x_2 : x_3) in CP^3 such that the determinant of the matrix x_0 A_1 + x_1 A_1 + x_2 A_2 + x_3 A_3 is zero) and a spectrahedron in the three dimensional real projective space RP^3 (the set of points (x_0 : x_1 : x_2 : x_3) in RP^3 such that the matrix x_0 A_1 + x_1 A_1 + x_2 A_2 + x_3 A_3 is semidefinite).
In general, the spectral surface considered has 10 double points. We show that the boundary of the spectrahedron cannot contain more than 8 doubles points of the spectral surface. The proof is based on a study of period spaces of real K3-surfaces.
Université de Strasbourg
will present
On Real Determinantal Quartics
Wednesday, February 10, 2010, 4:00pm
Ungar Room 402
Abstract: Let A_0, A_1, A_2, and A_3 be real symmetric 4 x 4 matrices. One can associate to these four matrices a spectral surface in the three dimensional complex projective space CP^3 (the set of points (x_0 : x_1 : x_2 : x_3) in CP^3 such that the determinant of the matrix x_0 A_1 + x_1 A_1 + x_2 A_2 + x_3 A_3 is zero) and a spectrahedron in the three dimensional real projective space RP^3 (the set of points (x_0 : x_1 : x_2 : x_3) in RP^3 such that the matrix x_0 A_1 + x_1 A_1 + x_2 A_2 + x_3 A_3 is semidefinite).
In general, the spectral surface considered has 10 double points. We show that the boundary of the spectrahedron cannot contain more than 8 doubles points of the spectral surface. The proof is based on a study of period spaces of real K3-surfaces.
