Seminario de Geometría Algebraica

Expositor: Michael Kemeny, University of Wisconsin-Madison.

Resumen: The classical work of Petri tells us that a canonical curve is an intersection of quadrics (with some exceptions) and, moreover, the theorem of Max Noether tells us how many such quadrics are needed to generate the ideal of the curve. It is natural to ask what one can say about these quadrics, and, indeed, in important work by Andreotti-Mayer in the 60s and Green in the 80s, it is established that the ideal is always generated by quadrics of rank four. Following Green's philosophy that one should generalize the classical work on the ideal of a projective variety to a study of the minimal free resolution of the ideal, we will show how to define a notion of rank for any linear syzygy. We then generalize Andreotti-Mayer-Green's result by proving that all linear syzygy spaces of a canonical curve are spanned by syzygies of the minimal possible rank.

https://www.matem.unam.mx/~lozano/eseminar.html