Vector Fields and the Cohomology Ring of Toric Varieties
2005 ◽
Vol 48
(3)
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pp. 414-427
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Keyword(s):
Zero Set
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AbstractLetXbe a smooth complex projective variety with a holomorphic vector field with isolated zero setZ. From the results of Carrell and Lieberman there exists a filtrationF0⊂F1⊂ · · · ofA(Z), the ring of ℂ-valued functions onZ, such thatas graded algebras. In this note, for a smooth projective toric variety and a vector field generated by the action of a 1-parameter subgroup of the torus, we work out this filtration. Our main result is an explicit connection between this filtration and the polytope algebra ofX.
2013 ◽
Vol 150
(3)
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pp. 369-395
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1999 ◽
Vol 42
(2)
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pp. 209-213
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Keyword(s):
2018 ◽
Vol 154
(7)
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pp. 1534-1570
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2019 ◽
Vol 22
(08)
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pp. 1950079
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2015 ◽
Vol 2015
(702)
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pp. 1-40
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2013 ◽
Vol 95
(3)
◽
pp. 315-328
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Keyword(s):
2020 ◽
Vol 58
(3)
◽
pp. 241-251