# 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.