Equations for secant varieties of Veronese and other varieties

Understand

New classes of modules of equations for secant varieties of Veronese varieties are defined using representation theory and geometry.

• Some old modules of equations (catalecticant minors) are revisited to determine when they are sufficient to give scheme-theoretic defining equations.
• An algorithm to decompose a general ternary quintic as the sum of seven fifth powers is given as an illustration of our methods.
• Our new equations and results about them are put into a larger context by introducing vector bundle techniques for finding equations of secant varieties in general.