The Plücker degree of the main component of the Quot scheme is computed via a decomposition of pushforward classes of powers of c1(O^[l]) in the Chow ring of the symmetric product, yielding its leading term and a higher-dimensional Schubert analogue.
On the Quot scheme $\mathrm{Quot}^{l}_{S}(\mathcal{E})$
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abstract
We study the geometry of the Quot scheme $\mathrm{Quot}^l_{S}(\mathcal{E})$ of length $l$ coherent sheaf quotients of a locally free sheaf $\mathcal{E}$ on a smooth projective surface $\mathrm{S}$. In particular, we investigate the nature of its singularities, its intersection theory, and the cohomology of sheaves on $\mathrm{Quot}^l_{S}(\mathcal{E})$.
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Pl\"ucker degrees of Quot schemes
The Plücker degree of the main component of the Quot scheme is computed via a decomposition of pushforward classes of powers of c1(O^[l]) in the Chow ring of the symmetric product, yielding its leading term and a higher-dimensional Schubert analogue.