arXiv 0803.01602008-03math.ACmath.AG

A Bound for Orders in Differential Nullstellensatz

Oleg Golubitsky, Marina Kondratieva, Alexey Ovchinnikov, Agnes Szanto

备注：: 25 pages; improved bound; simplified main argument; more detailed proofs
发表信息：: Journal of Algebra, Volume 322, Issue 11, 2009, pp 3852-3877
DOI：: 10.1016/j.jalgebra.2009.05.032

英文摘要：

We give the first known bound for orders of differentiations in differential Nullstellensatz for both partial and ordinary algebraic differential equations. This problem was previously addressed by A. Seidenberg but no complete solution was given. Our result is a complement to the corresponding result in algebraic geometry, which gives a bound on degrees of polynomial coefficients in effective Nullstellensatz.

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