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| dc.contributor | Miró-Roig, Rosa M. (Rosa Maria) | |
| dc.creator | Colarte Gómez, Liena | |
| dc.date | 2017-06-28T10:30:15Z | |
| dc.date | 2017-06-28T10:30:15Z | |
| dc.date | 2017-01-17 | |
| dc.date.accessioned | 2024-12-16T10:24:33Z | |
| dc.date.available | 2024-12-16T10:24:33Z | |
| dc.identifier | http://hdl.handle.net/2445/113012 | |
| dc.identifier.uri | http://fima-docencia.ub.edu:8080/xmlui/handle/123456789/17903 | |
| dc.description | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Rosa Maria Miró-Roig | |
| dc.description | 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. | |
| dc.format | 75 p. | |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.rights | cc-by-nc-nd (c) Liena Colarte Gómez, 2017 | |
| dc.rights | http://creativecommons.org/licenses/by-nc-nd/3.0/es | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.source | Treballs Finals de Grau (TFG) - Matemàtiques | |
| dc.subject | Àlgebres de Hopf | |
| dc.subject | Treballs de fi de grau | |
| dc.subject | Àlgebra multilineal | |
| dc.subject | Combinatòria (Matemàtica) | |
| dc.subject | Grups algebraics lineals | |
| dc.subject | Hopf algebras | |
| dc.subject | Bachelor's theses | |
| dc.subject | Multilinear algebra | |
| dc.subject | Combinations | |
| dc.subject | Linear algebraic groups | |
| dc.title | The Schur functors and the resolution of determinantal varieties | |
| dc.type | info:eu-repo/semantics/bachelorThesis |
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