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TitleOn the complexity of counting components of algebraic varieties
Author(s) Peter Bürgisser, Peter Scheiblechner
TypeArticle in Journal
AbstractWe give a uniform method for the two problems of counting the connected and irreducible components of complex algebraic varieties. Our algorithms are purely algebraic, i.e., they use only the field structure of C . They work in parallel polynomial time, i.e., they can be implemented by algebraic circuits of polynomial depth. The design of our algorithms relies on the concept of algebraic differential forms. A further important building block is an algorithm of Szántó computing a variant of characteristic sets. Furthermore, we use these methods to obtain a parallel polynomial time algorithm for computing the Hilbert polynomial of a projective variety which is arithmetically Cohen–Macaulay.
KeywordsCharacteristic sets, Complexity, Connected components, Differential forms, Irreducible components
URL http://www.sciencedirect.com/science/article/pii/S0747717109000133
JournalJournal of Symbolic Computation
Pages1114 - 1136
NoteEffective Methods in Algebraic Geometry
Translation No
Refereed No