| Abstract |
This talk explores the intricate interplay between the intrinsic geometry of complex projective varieties
and the homological invariants of their defining ideals. We focus on the structure of syzygies—encoding higher
order algebraic relations among defining equations—and the Castelnuovo–Mumford regularity, a key invariant
governing the complexity of embedded varieties. Finally, we survey classic and recent developments regarding
linear syzygies, the status of the Eisenbud–Goto conjecture, and the higher syzygies of secant varieties. |
