Some algebraic sets of high local cohomological dimension in projective space
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- by Gennady Lyubeznik
- Proc. Amer. Math. Soc. 95 (1985), 9-10
- DOI: https://doi.org/10.1090/S0002-9939-1985-0796437-3
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Abstract:
Let ${V_0}, \ldots ,{V_{[n/t]}}$ be algebraic sets of pure codimension $t$ in ${P^n}$, and suppose $\cap {V_i}$ is empty. Then ${P^n} - \cup {V_i}$ has cohomological dimension $n - [n/t]$.References
- Gerd Faltings, Über lokale Kohomologiegruppen hoher Ordnung, J. Reine Angew. Math. 313 (1980), 43–51 (German). MR 552461, DOI 10.1515/crll.1980.313.43
- Robin Hartshorne, Cohomological dimension of algebraic varieties, Ann. of Math. (2) 88 (1968), 403–450. MR 232780, DOI 10.2307/1970720
- Gennady Lyubeznik, On set-theoretic intersections, J. Algebra 87 (1984), no. 1, 105–112. MR 736771, DOI 10.1016/0021-8693(84)90162-5 —, Set-theoretic intersections and monomial ideals, Thesis, Columbia University, 1984.
Bibliographic Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 95 (1985), 9-10
- MSC: Primary 14B15; Secondary 13D99
- DOI: https://doi.org/10.1090/S0002-9939-1985-0796437-3
- MathSciNet review: 796437