University of Sydney Algebra Seminar

Alexandru Dimca (University of Nice)

Friday 30 March, 12:05-12:55pm, Carslaw 175

Jacobian ideal: syzygies and Hodge theory

If \(f\) is a homogeneous polynomials defining a smooth projective hypersurface \(V\), then it is known that the partial derivatives of \(f\) form a regular sequence, hence there are no nontrivial syzygies. When the hypersurface \(V\) has isolated singularities, one can give lower bounds for the degrees of no nontrivial syzygies and relate them to some nonzero Betti numbers.