Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/113012
 Title: The Schur functors and the resolution of determinantal varieties Author: Colarte Gómez, Liena Director: Miró-Roig, Rosa M. (Rosa Maria) Keywords: Àlgebres de HopfTreballs de fi de grauÀlgebra multilinealCombinatòria (Matemàtica)Grups algebraics linealsHopf algebrasBachelor's thesisMultilinear algebraCombinationsLinear algebraic groups Issue Date: 17-Jan-2017 Abstract: Resolutions is one of the most effective methods to obtain information about varieties in Algebraic Geometry. For many years there has been considerable efforts in finding a resolution of determinantal varieties. To put the problem plainly, assume $R=K[x_{0},...,x_{s}]$ is the polynomial ring over an algebraically closed field of characteristic zero and $\mathbb{P}^{s}$ is the projective space of dimension $s$ over $K$. Given $(r_{i,j})$ a homogeneous matrix of size $pxq$ with entries in $R$, the problem is to find an explicit minimal free resolution of the ideal $I_{t}$ defined by the $txt$ minors of this matrix. Over certain hypothesis on $I_{t}$ , this is a minimal free resolution of the variety \$X={z \in\mathbb{P}s|rg((r_{i,j})(z))

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