Algebraic Geometry Seminar
Sijong Kwak
KAIST(Korea Advanced Institute of Science and Technology)
Sharp upper bounds of the graded Betti numbers and classifications
Abstract: For a projective variety (or scheme), the graded Betti numbers are defined from either
the minimal free resolution of the homogeneous coordinate ring or the Koszul complex.
These extrinsic numbers measure the complexity of the relations between the defining equations
and reflect the intrinsic and geometric information on a variety. In this talk, I'd like to introduce
the results of Castelnuovo and Fano on quadric equations and generalize them to the higher linear
syzygies in the first strand.
As a consequence, I'd like to characterize varieties of minimal degree and Del Pezzo varieties
with respect to linear syzygies. Main ideas are inner projections, mapping cone and partial
elimination ideals due to M. Green.
Wednesday November 18, 2015 at 4:00 PM in SEO 427