Geodesic
𝐿²-cohomology, Nash blowup and semismall resolutions
Journal of the American Mathematical Society, Tome 06 (1993) no. 4, pp. 817-824

Voir la notice de l'article provenant de la source American Mathematical Society

We study the structure of ${L^2}$-forms on singular complex projective varieties with respect to Fubini-Studi metric using resolution of singularities. We show that a semismall resolution of $X$ has to be small if it can be mapped onto the Nash blowup of $X$. 
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Youssin, Boris. 𝐿²-cohomology, Nash blowup and semismall resolutions. Journal of the American Mathematical Society, Tome 06 (1993) no. 4, pp. 817-824. doi: 10.1090/S0894-0347-1993-1213798-4

[1] Cheeger, Jeff, Goresky, Mark, Macpherson, Robert 𝐿²-cohomology and intersection homology of singular algebraic varieties 1982 303 340

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[3] Goresky, Mark, Macpherson, Robert Intersection homology. II Invent. Math. 1983 77 129

[4] Ohsawa, Takeo On the 𝐿² cohomology of complex spaces Math. Z. 1992 519 530

[5] Teissier, Bernard Variétés polaires. II. Multiplicités polaires, sections planes, et conditions de Whitney 1982 314 491

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