Moduli spaces of quasitrivial rank 2 sheaves

Abstract: Douglas Guimarães (UNICAMP)

Title: Moduli spaces of quasitrivial rank 2 sheaves

Abstract: A torsion free sheaf $E$ on $\mathbb{P}^3$ is called quasitrivial if $E^{\vee\vee}=\mathcal{O}_{\mathbb{P}^3}^{\oplus r}$ and $\dim(E^{\vee\vee}/E)=0$. While such sheaves are always $\mu$-semistable, they may not be Gieseker semistable. We study the moduli spaces of $\mu$- and Gieseker semistable quasitrivial sheaves of rank 2 via the quot scheme of points $Quot(\mathcal{O}_{\mathbb{P}^3}^{\oplus 2},n)$, where $n=h^0(E^{\vee\vee}/E)$. We will show the construction of an irreducible component of the Gieseker moduli space which is birrational to the total space of a $\mathbb{P}^{n-1}$-bundle over $S(n-1)\times\mathbb{P}^3$, where $S(n)$ is the smoothable component of the Hilbert scheme of $n$ points in $ \mathbb{P}^3$. Furthermore, this is the only irreducible component when $n\le10$.

algebraic geometry

Audience: researchers in the topic

Brazilian algebraic geometry seminar

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