Reflexive pull-backs and base extension
Authors:
Brendan Hassett and Sándor J. Kovács
Journal:
J. Algebraic Geom. 13 (2004), 233-247
DOI:
https://doi.org/10.1090/S1056-3911-03-00331-X
Published electronically:
September 24, 2003
MathSciNet review:
2047697
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Abstract |
References |
Additional Information
Abstract: We prove that Viehweg’s moduli functor of stable surfaces is locally closed.
Alexeev94 V. A. Alexeev, Boundedness and $K^2$ for log surfaces, Internat. J. Math. 5 (1994), no. 6, 779–810.
Bruns-Herzog93 W. Bruno and J. Herzog, Cohen-Macaulay Rings, Cambridge Univ. Press, 1993.
Conrad00 B. Conrad, Grothendieck duality and base change, Lecture Notes in Mathematics, 1750, Springer-Verlag, 2000.
Eisenbud95 D. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Springer-Verlag, New York, 1995.
EGA A. Grothendieck and J. Dieudonné, Eléments de Géométrie Algébrique, Inst. Hautes Études Sci. Publ. Math. 4, 8, 11, 17, 20, 24, 28, 32, 1960–67.
Hartshorne77 R. Hartshorne, Algebraic Geometry, Springer-Verlag, New York-Heidelberg, 1977.
Hassett01 B. Hassett, Stable limits of log surfaces and Cohen-Macaulay singularities, J. Algebra 242 (2001) no. 1, 225–235.
Karu00 K. Karu, Minimal models and boundedness of stable varieties, J. Algebraic Geom. 9 (2000), no. 1, 93–109.
Kleiman80 S. Kleiman, Relative duality for quasicoherent sheaves, Compositio Math. 41 (1980), no. 1, 39–60.
Kollar85 J. Kollár, Toward moduli of singular varieties, Compositio Math. 56 (1985), no.3, 369–398.
Kollar90 J. Kollár, Projectivity of complete moduli, J. Differential Geom. 32 (1990), no. 1, 235–268.
Kollar94 J. Kollár, Push forward and base change for open immersions, unpublished manuscript, 1994.
KSB88 J. Kollár and N. Shepherd-Barron, Threefolds and deformations of surface singularities, Invent. Math. 91 (1988), no. 2, 299–338.
Viehweg95 E. Viehweg, Quasi-Projective Moduli of Polarized Manifolds, Springer-Verlag, Berlin, 1995.
Alexeev94 V. A. Alexeev, Boundedness and $K^2$ for log surfaces, Internat. J. Math. 5 (1994), no. 6, 779–810.
Bruns-Herzog93 W. Bruno and J. Herzog, Cohen-Macaulay Rings, Cambridge Univ. Press, 1993.
Conrad00 B. Conrad, Grothendieck duality and base change, Lecture Notes in Mathematics, 1750, Springer-Verlag, 2000.
Eisenbud95 D. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Springer-Verlag, New York, 1995.
EGA A. Grothendieck and J. Dieudonné, Eléments de Géométrie Algébrique, Inst. Hautes Études Sci. Publ. Math. 4, 8, 11, 17, 20, 24, 28, 32, 1960–67.
Hartshorne77 R. Hartshorne, Algebraic Geometry, Springer-Verlag, New York-Heidelberg, 1977.
Hassett01 B. Hassett, Stable limits of log surfaces and Cohen-Macaulay singularities, J. Algebra 242 (2001) no. 1, 225–235.
Karu00 K. Karu, Minimal models and boundedness of stable varieties, J. Algebraic Geom. 9 (2000), no. 1, 93–109.
Kleiman80 S. Kleiman, Relative duality for quasicoherent sheaves, Compositio Math. 41 (1980), no. 1, 39–60.
Kollar85 J. Kollár, Toward moduli of singular varieties, Compositio Math. 56 (1985), no.3, 369–398.
Kollar90 J. Kollár, Projectivity of complete moduli, J. Differential Geom. 32 (1990), no. 1, 235–268.
Kollar94 J. Kollár, Push forward and base change for open immersions, unpublished manuscript, 1994.
KSB88 J. Kollár and N. Shepherd-Barron, Threefolds and deformations of surface singularities, Invent. Math. 91 (1988), no. 2, 299–338.
Viehweg95 E. Viehweg, Quasi-Projective Moduli of Polarized Manifolds, Springer-Verlag, Berlin, 1995.
Additional Information
Brendan Hassett
Affiliation:
Department of Mathematics–MS 136, Rice University, 6100 S. Main St., Houston Texas 77005-1892
Email:
hassett@math.rice.edu
Sándor J. Kovács
Affiliation:
Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195
MR Author ID:
289685
Email:
kovacs@math.washington.edu
Received by editor(s):
August 8, 2001
Published electronically:
September 24, 2003
Additional Notes:
The first author was supported in part by an NSF Postdoctoral Fellowship, NSF Grant DMS-0070537, and the Institute of Mathematical Sciences of the Chinese University of Hong Kong. The second author was supported in part by NSF Grants DMS-019607 and DMS-0092165.
