论文标题
非标准的仿射品种连续性证明
A nonstandard proof of continuity of affine varieties
论文作者
论文摘要
扩展经典的结果，即多项式的根部具有$ \ mathbf {c} $是多项式，非标准分析系数的连续函数，以证明，如果$ \ mathcal {f} = \ {f_λ：λ：λ：λ：λ\inλ：λ $ \ mathbf {c} [t_1，\ ldots，t_n] $，如果$^*\ Mathcal {g} = \ {g_λ\inλ\} $是$^*\ Mathbf {c} $ is AN $ _0 $ _0 $ _1，t_1，\ ld]，是一组polynomials所有$λ\在λ$中的$f_λ$的无限变形，然后非标准仿射品种$^*v_0（\ Mathcal {g}）$是仿射品种$ v（\ Mathcal {f}）$的无限变形。
Extending the classical result that the roots of a polynomial with coefficients in $\mathbf{C}$ are continuous functions of the coefficients of the polynomial, nonstandard analysis is used to prove that if $\mathcal{F} = \{f_λ :λ\in Λ\}$ is a set of polynomials in $\mathbf{C}[t_1,\ldots, t_n]$ and if $^*\mathcal{G} = \{g_λ :λ\in Λ\}$ is a set of polynomials in $^*\mathbf{C}_0[t_1,\ldots, t_n]$ such that $g_λ$ is an infinitesimal deformation of $f_λ$ for all $λ\in Λ$, then the nonstandard affine variety $^*V_0(\mathcal{G})$ is an infinitesimal deformation of the affine variety $V(\mathcal{F})$.
