论文标题
某些引号方案的无限变形
Infinitesimal deformations of some Quot schemes
论文作者
论文摘要
让$ e $为平滑的复杂的投影曲线$ c $至少两个。令$ \ Mathcal {q}（e，d）$为引号方案参数化$ e $ of度量$ d $的扭转商。我们计算切线束的共同体$ t _ {\ Mathcal {q}（e，d）} $。特别是，计算了$ \ Mathcal {q}（e，d）$的无限变形的空间。 Kempf和Fantechi计算了$ \ Mathcal {q}（\ Mathcal {o} _C，d）\，= \，c^{（d）} $的无限变形空间。我们还明确描述了$ \ Mathcal {q}（e，d）$的无穷小变形。
Let $E$ be a vector bundle on a smooth complex projective curve $C$ of genus at least two. Let $\mathcal{Q}(E,d)$ be the Quot scheme parameterizing the torsion quotients of $E$ of degree $d$. We compute the cohomologies of the tangent bundle $T_{\mathcal{Q}(E,d)}$. In particular, the space of infinitesimal deformations of $\mathcal{Q}(E,d)$ is computed. Kempf and Fantechi computed the space of infinitesimal deformations of $\mathcal{Q}(\mathcal{O}_C,d)\,=\, C^{(d)}$. We also explicitly describe the infinitesimal deformations of $\mathcal{Q}(E,d)$.
