论文标题
Hinstanton捆绑夹在三维偏振射击品种上
H-instanton bundles on three-dimensional polarized projective varieties
论文作者
论文摘要
我们提出了一个instanton捆绑包（称为$ h $ -instanton捆绑包）的概念，这些尺寸的三个尺寸三个尺寸都被一个非常大的除数$ h $两极化，从而自然而然地将其概括为$ \ mathbb {p}^3 $，并且在flag trag trag trag trag tright $ f（0,1,1,2）上。我们讨论了Veronese和Fano三倍的案例。然后，我们处理$ h $ -instanton捆绑$ \ MATHCAL {E} $上的三维合理正常卷轴$ s（a_0，a_1，a_2）$。我们提供了$ h $ -instanton捆绑包的单一描述，我们证明了$ s（a_0，a_1，a_2）$的$μ$ stable $ h $ -instanton捆绑包，用于任何可接受的费用$ k = c_2（\ mathcal {e}）h $。然后，我们使用$ s（a，a，b）$和$ s（a_0，a_1，a_2）$进行更详细的详细处理，其中$ a_0+a_1> a_2 $甚至是学位。最后，我们描述了$μ$稳定的束的模量空间的一个不错的组成部分，其点代表$ h $ -instantons。
We propose a notion of instanton bundle (called $H$-instanton bundle) on any projective variety of dimension three polarized by a very ample divisor $H$, that naturally generalizes the ones on $\mathbb{P}^3$ and on the flag threefold $F(0,1,2)$. We discuss the cases of Veronese and Fano threefolds. Then we deal with $H$-instanton bundles $\mathcal{E}$ on three-dimensional rational normal scrolls $S(a_0,a_1,a_2)$. We give a monadic description of $H$-instanton bundles and we prove the existence of $μ$-stable $H$-instanton bundles on $S(a_0,a_1,a_2)$ for any admissible charge $k=c_2(\mathcal{E})H$. Then we deal in more detail with $S(a,a,b)$ and $S(a_0,a_1,a_2)$ with $a_0+a_1>a_2$ and even degree. Finally we describe a nice component of the moduli space of $μ$-stable bundles whose points represent $H$-instantons.
