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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| Lenguaje: | English |
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Universidad de La Frontera. Departamento de Matemática y Estadística.
2010
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oai:scielo:S0719-064620100001000172018-10-08Projective Squares in and Bott’s Localization FormulaRojas,JacquelineMendoza,RamónSilva,Eben da Hilbert scheme 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 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.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.12 n.1 20102010-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000100017en10.4067/S0719-06462010000100017 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
Hilbert scheme Bott’s localization formula |
| spellingShingle |
Hilbert scheme Bott’s localization formula Rojas,Jacqueline Mendoza,Ramón Silva,Eben da Projective Squares in and Bott’s Localization Formula |
| description |
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. |
| author |
Rojas,Jacqueline Mendoza,Ramón Silva,Eben da |
| author_facet |
Rojas,Jacqueline Mendoza,Ramón Silva,Eben da |
| author_sort |
Rojas,Jacqueline |
| title |
Projective Squares in and Bott’s Localization Formula |
| title_short |
Projective Squares in and Bott’s Localization Formula |
| title_full |
Projective Squares in and Bott’s Localization Formula |
| title_fullStr |
Projective Squares in and Bott’s Localization Formula |
| title_full_unstemmed |
Projective Squares in and Bott’s Localization Formula |
| title_sort |
projective squares in and bott’s localization formula |
| publisher |
Universidad de La Frontera. Departamento de Matemática y Estadística. |
| publishDate |
2010 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000100017 |
| work_keys_str_mv |
AT rojasjacqueline projectivesquaresinandbottrsquoslocalizationformula AT mendozaramon projectivesquaresinandbottrsquoslocalizationformula AT silvaebenda projectivesquaresinandbottrsquoslocalizationformula |
| _version_ |
1714206764539314176 |