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Register a new userDegree of the generalized Plucker embedding of a Quot scheme and Quantum cohomology
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We compute the degree of the generalized Plucker embedding $kappa$ of a Quot scheme $X$ over $PP^1$. The space $X$ can also be considered as a compactification of the space of algebraic maps of a fixed degree from $PP^1$ to the Grassmanian $rm{Grass}(m,n)$. Then the degree of the embedded variety $kappa (X)$ can be interpreted as an intersection product of pullbacks of cohomology classes from $rm{Grass}(m,n)$ through the map $psi$ that evaluates a map from $PP^1$ at a point $xin PP^1$. We show that our formula for the degree verifies the formula for these intersection products predicted by physicists through Quantum cohomology~cite{va92}~cite{in91}~cite{wi94}. We arrive at the degree by proving a version of the classical Pieris formula on the variety $X$, using a cell decomposition of a space that lies in between $X$ and $kappa (X)$.
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