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Singularities of generic projection hypersurfaces
Author(s):
Davis
C.
Doherty
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2407-2415.
MSC (2000):
Primary 14J17;
Secondary 14E15, 14B05.
Posted:
February 20, 2008
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Additional information
Abstract:
Linearly projecting smooth projective varieties provide a method of obtaining hypersurfaces birational to the original varieties. We show that in low dimension, the resulting hypersurfaces only have Du Bois singularities. Moreover, we conclude that these Du Bois singularities are in fact semi log canonical. However, we demonstrate the existence of counterexamples in high dimension - the generic linear projection of certain varieties of dimension 30 or higher is neither semi log canonical nor Du Bois.
References:
-
- [DB81]
- P. DU BOIS: Complexe de de Rham filtré d'une variété singulière, Bull. Soc. Math. France 109 (1981), no. 1, 41-81. MR 613848 (82j:14006)
- [Fed83]
- R. FEDDER:
 -purity and rational singularity, Trans. Amer. Math. Soc. 278 (1983), no. 2, 461-480. MR 701505 (84h:13031) - [GT80]
- S. GRECO AND C. TRAVERSO: On seminormal schemes, Compositio Math. 40 (1980), no. 3, 325-365. MR 571055 (81j:14030)
- [Har77]
- R. HARTSHORNE: Algebraic geometry, Springer-Verlag, New York, 1977. MR 0463157 (57:3116)
- [Kol90]
- J. KOLLáR: Projectivity of complete moduli, J. Differential Geom. 32 (1990), no. 1, 235-268. MR 1064874 (92e:14008)
- [Kol92]
- J. KOLLáR ET AL.: Flips and abundance for algebraic threefolds, Société Mathématique de France, Paris, 1992. MR 94f:14013
- [Kov99]
- S. KOVáCS: Rational, log canonical, Du Bois singularities: on the conjectures of Kollár and Steenbrink, Compositio Math. 118 (1999), no. 2, 123-133. MR 1713307 (2001g:14022)
- [Laz04a]
- R. LAZARSFELD: Positivity in algebraic geometry. I, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 48, Springer-Verlag, Berlin, 2004, Classical setting: Line bundles and linear series. MR 2095471 (2005k:14001a)
- [Laz04b]
- R. LAZARSFELD: Positivity in algebraic geometry. II, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 49, Springer-Verlag, Berlin, 2004, Positivity for vector bundles, and multiplier ideals. MR 2095472 (2005k:14001b)
- [Rob71]
- J. ROBERTS: Generic projections of algebraic varieties, Amer. J. Math. 93 (1971), 191-214. MR 0277530 (43:3263)
- [Rob75]
- J. ROBERTS: Singularity subschemes and generic projections, Trans. Amer. Math. Soc. 212 (1975), 229-268. MR 0422274 (54:10265)
- [Sch06]
- K. SCHWEDE: On f-injective and Du Bois singularities, Ph.D. thesis, University of Washington, 2006.
- [Ste81]
- J. H. M. STEENBRINK: Cohomologically insignificant degenerations, Compositio Math. 42 (1980/81), no. 3, 315-320. MR 607373 (84g:14011)
- [ZL86]
- M. G. ZAĬDENBERG AND V. Y. LIN: Finiteness theorems for holomorphic mappings, Current problems in mathematics. Fundamental directions, Vol. 9 (Russian), Itogi Nauki i Tekhniki, Akad. Nauk SSSR Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1986, pp. 127-193, 272. MR 860611
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Additional Information:
Davis
C.
Doherty
Affiliation:
Department of Mathematics, University of Washington, Seattle, Washington 98195
Address at time of publication:
Department of Mathematics, Seattle University, Seattle, Washington 98122
DOI:
10.1090/S0002-9939-08-09286-1
PII:
S 0002-9939(08)09286-1
Received by editor(s):
June 11, 2007,
Received by editor(s) in revised form:
June 20, 2007
Posted:
February 20, 2008
Communicated by:
Ted Chinburg
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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