Picard Groups of Some Quot Schemes

Abstract

Let $C$ be a smooth projective curve over the field of complex numbers $\mathbb{C}$ of genus $g(C)>0$. Let $E$ be a locally free sheaf on $C$ of rank $r$ and degree $e$. Let $\mathcal{Q}:={\rm Quot}_{C/\mathbb{C}}(E,k,d)$ denote the Quot scheme of quotients of $E$ of rank $k$ and degree $d$. For $k>0$ and $d\gg 0$ we compute the Picard group of $\mathcal{Q}$.

Theorems & Definitions (50)

• Theorem 1.2: Theorem \ref{['picard group of Quot']}
• Theorem 1.3: Theorem \ref{['Q_L is locally factorial']}
• Theorem 1.4: Theorem \ref{['Picard group of Q_L']}
• Lemma 2.1
• proof
• Lemma 2.2
• proof
• Lemma 2.7
• proof
• Lemma 3.2