On a generalization of Stickelberger's Theorem

We prove two versions of Stickelberger’s Theorem for positive dimensions and use them to compute the connected and irreducible components of a complex algebraic variety. If the variety is given by polynomials of degree ≤ d in n variables, then our algorithms run in parallel (sequential) time (n log d)O(1) (dO(n4 ) ). In the case of a hypersurface the complexity drops to O(n2 log2 d) (dO(n) ). In the proof of the last result we use the effective Nullstellensatz for two polynomials, which we also prove by very elementary methods. Key words: Stickelberger’s Theorem, connected components, irreducible components, effective Nullstellensatz

• Type: Journal
• Year: 2010
• Where: JSC
• Authors: Peter Scheiblechner
• Keywords: Complex Algebraic Variety, Effective Nullstellensatz, Irreducible Components, JSC 2010