Projective Squares in and Bott’s Localization Formula
We give an explicit description of the Hilbert scheme that parametrizes the closed 0-dimensional subschemes of degree 4 in the projective plane that allows us to afford a natural embedding in a product of Grassmann varieties. We also use this description to explain how to apply Bott’s loca...
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| Autores principales: | , , |
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| Lenguaje: | English |
| Publicado: |
Universidad de La Frontera. Departamento de Matemática y Estadística.
2010
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000100017 |
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| Sumario: | We give an explicit description of the Hilbert scheme that parametrizes the closed 0-dimensional subschemes of degree 4 in the projective plane that allows us to afford a natural embedding in a product of Grassmann varieties. We also use this description to explain how to apply Bott’s localization formula (introduced in 1967 in Bott’s work [2]) to give an answer for an enumerative question as used by the first time by Ellingsrud and Str<img border=0 width=12 height=15 src="http:/fbpe/img/cubo/v12n1/img47.jpg">mme in [8] to compute the number of twisted cubics on a general Calabi-Yau threefold which is a complete intersection in some projective space and used later by Kontsevich in [16] to count rational plane curves of degree d passing through 3d - 1 points in general position in the plane. |
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