Journal of the American Mathematical Society

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ISSN 1088-6834(e) ISSN 0894-0347(p)

-cohomology, Nash blowup and semismall resolutions

Author(s): Boris Youssin
Journal: J. Amer. Math. Soc. 6 (1993), 817-824.
MSC: Primary 32S45; Secondary 14E15, 32S60
MathSciNet review: 1213798
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Abstract | References | Similar articles | Additional information

Abstract: 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 has to be small if it can be mapped onto the Nash blowup of .

References:

[CGM]: J. Cheeger, M. Goresky, and R. MacPherson, ${L^2}$ -cohomology and intersection cohomology of singular algebraic varieties, Seminar on differential geometry (S. T. Yau, ed.), Princeton Univ. Press, Princeton, NJ, 1982, pp. 303-340. MR 645745 (84f:58005)
[HP]: W. C. Hsiang and V. Pati, ${L^2}$ -cohomology of normal algebraic surfaces. I, Invent. Math. 81 (1985), 395-412. MR 807064 (87f:32024)
[GM]: M. Goresky and R. MacPherson, Intersection homology. II, Invent. Math. 71 (1983), 77-129. MR 696691 (84i:57012)
[Ohsawa]: T. Ohsawa, On the ${L^2}$ cohomology of complex spaces, Math. Z. 209 (1992), 519-530. MR 1156434 (93d:32063)
[Teissier]: B. Teissier, Variétés polaires. II: Multiplicités polaires, sections planes, et conditions de Whitney, Actes de la conférance de géometrie algébrique á la Rábida, Lecture Notes in Math., vol. 961, 1981, pp. 314-491. MR 708342 (85i:32019)

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