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DC Field | Value | Language |
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dc.contributor.advisor | Miró-Roig, Rosa M. (Rosa Maria) | - |
dc.contributor.author | Colarte Gómez, Liena | - |
dc.date.accessioned | 2017-06-28T10:30:15Z | - |
dc.date.available | 2017-06-28T10:30:15Z | - |
dc.date.issued | 2017-01-17 | - |
dc.identifier.uri | http://hdl.handle.net/2445/113012 | - |
dc.description | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Rosa Maria Miró-Roig | ca |
dc.description.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 $X={z \in\mathbb{P}s|rg((r_{i,j})(z))<t} of \mathbb{P}^s$. It provides the Hilbert polynomial of $X$, the projective dimension and the arithmetically Cohen-Macaulayness of the variety among others characteristics. | ca |
dc.format.extent | 75 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | ca |
dc.rights | cc-by-nc-nd (c) Liena Colarte Gómez, 2017 | - |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es | - |
dc.source | Treballs Finals de Grau (TFG) - Matemàtiques | - |
dc.subject.classification | Àlgebres de Hopf | - |
dc.subject.classification | Treballs de fi de grau | - |
dc.subject.classification | Àlgebra multilineal | ca |
dc.subject.classification | Combinatòria (Matemàtica) | ca |
dc.subject.classification | Grups algebraics lineals | ca |
dc.subject.other | Hopf algebras | - |
dc.subject.other | Bachelor's theses | - |
dc.subject.other | Multilinear algebra | en |
dc.subject.other | Combinations | en |
dc.subject.other | Linear algebraic groups | en |
dc.title | The Schur functors and the resolution of determinantal varieties | ca |
dc.type | info:eu-repo/semantics/bachelorThesis | ca |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
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memoria.pdf | Memòria | 486.41 kB | Adobe PDF | View/Open |
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