@article {IOPORT.05859491,
    author       = {Chistov, A.L.},
    title        = {Double-exponential lower bound for the degree of any system of generators of a polynomial prime ideal.},
    year         = {2009},
    journal      = {St. Petersburg Mathematical Journal},
    volume       = {20},
    number       = {6},
    issn         = {1061-0022},
    pages        = {983-1001},
    publisher    = {American Mathematical Society, Providence, RI},
    doi          = {10.1090/S1061-0022-09-01081-4},
    abstract     = {Summary: Let $ A$ be a polynomial ring in $ n+1$ variables over an arbitrary infinite field $ k$. It is proved that for all sufficiently large $ n$ and $ d$ there is a homogeneous prime ideal $ {\mathfrak{p}}\subset A$ satisfying the following conditions. The ideal $ {\mathfrak{p}}$ corresponds to a component, defined over $ k$ and irreducible over $ \overline{k}$, of a projective algebraic variety given by a system of homogeneous polynomial equations with polynomials in $ A$ of degrees less than $ d$. Any system of generators of $ {\mathfrak{p}}$ contains a polynomial of degree at least $ d^{2^{cn}}$ for an absolute constant $ c>0$, which can be computed efficiently. This solves an important old problem in effective algebraic geometry. For the case of finite fields a slightly less strong result is obtained.},
    identifier   = {05859491},
}