On the Quot scheme ${\mathrm{Quot}}_{{\mathcal{O}}_{{\mathbb{P}}^1}^r/{\mathbb{P}}^1/k}^d$

Cristina Bertone, Steven L. Kleiman, Margherita Roggero

We consider the quot scheme ${\mathrm{Quot}}_{{\mathcal{F}}^r/{\mathbb{P}}^1/k}^d$ of locally free quotients of ${\mathcal{F}}^r:={⨁}^r{\mathcal{O}}_{{\mathbb{P}}^1}$ with Hilbert po…