| 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 |
2024-12-16T10:24:36Z |
|
| dc.date.available |
2024-12-16T10:24:36Z |
|
| dc.identifier |
http://hdl.handle.net/2445/113012 |
|
| dc.identifier.uri |
http://fima-docencia.ub.edu:8080/xmlui/handle/123456789/17988 |
|
| 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 |
|