A note on the effective non-vanishing conjecture
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- by Qihong Xie
- Proc. Amer. Math. Soc. 137 (2009), 61-63
- DOI: https://doi.org/10.1090/S0002-9939-08-09539-7
- Published electronically: August 4, 2008
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Abstract:
We give a reduction of the irregular case for the effective non-vanishing conjecture by virtue of the Fourier-Mukai transform. As a consequence, we reprove that the effective non-vanishing conjecture holds on algebraic surfaces.References
- F. Ambro, Ladders on Fano varieties, J. Math. Sci. (New York) 94 (1999), no. 1, 1126–1135. Algebraic geometry, 9. MR 1703912, DOI 10.1007/BF02367253
- Jungkai A. Chen and Christopher D. Hacon, Linear series of irregular varieties, Algebraic geometry in East Asia (Kyoto, 2001) World Sci. Publ., River Edge, NJ, 2002, pp. 143–153. MR 2030451, DOI 10.1142/9789812705105_{0}004
- Yujiro Kawamata, On effective non-vanishing and base-point-freeness, Asian J. Math. 4 (2000), no. 1, 173–181. Kodaira’s issue. MR 1802918, DOI 10.4310/AJM.2000.v4.n1.a11
- Yujiro Kawamata, Katsumi Matsuda, and Kenji Matsuki, Introduction to the minimal model problem, Algebraic geometry, Sendai, 1985, Adv. Stud. Pure Math., vol. 10, North-Holland, Amsterdam, 1987, pp. 283–360. MR 946243, DOI 10.2969/aspm/01010283
- János Kollár and Shigefumi Mori, Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, vol. 134, Cambridge University Press, Cambridge, 1998. With the collaboration of C. H. Clemens and A. Corti; Translated from the 1998 Japanese original. MR 1658959, DOI 10.1017/CBO9780511662560
- Shigeru Mukai, Duality between $D(X)$ and $D(\hat X)$ with its application to Picard sheaves, Nagoya Math. J. 81 (1981), 153–175. MR 607081
- Mircea Mustaţă, Vanishing theorems on toric varieties, Tohoku Math. J. (2) 54 (2002), no. 3, 451–470. MR 1916637
- Giuseppe Pareschi and Mihnea Popa, Regularity on abelian varieties. I, J. Amer. Math. Soc. 16 (2003), no. 2, 285–302. MR 1949161, DOI 10.1090/S0894-0347-02-00414-9
- G. Pareschi, M. Popa, M-regularity and the Fourier-Mukai transform, preprint, math.AG/0512645.
- G. Pareschi, M. Popa, GV-sheaves, Fourier-Mukai transform, and generic vanishing, preprint, math.AG/0608127.
- Qihong Xie, On pseudo-effectivity of the second Chern classes for terminal threefolds, Asian J. Math. 9 (2005), no. 1, 121–132. MR 2150695
- Qihong Xie, Effective non-vanishing for algebraic surfaces in positive characteristic, J. Algebra 305 (2006), no. 2, 1111–1127. MR 2266872, DOI 10.1016/j.jalgebra.2006.06.008
Bibliographic Information
- Qihong Xie
- Affiliation: Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro, Tokyo 152-8551, Japan
- Address at time of publication: Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Meguro, Tokyo 153-8914, Japan
- Email: xie_qihong@hotmail.com
- Received by editor(s): January 17, 2007
- Received by editor(s) in revised form: October 18, 2007, November 16, 2007, and December 27, 2007
- Published electronically: August 4, 2008
- Communicated by: Ted Chinburg
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 61-63
- MSC (2000): Primary 14E30
- DOI: https://doi.org/10.1090/S0002-9939-08-09539-7
- MathSciNet review: 2439425