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A Non-vanishing Theorem of Del Pezzo Surfaces

Published online by Cambridge University Press:  03 March 2016

Chin-Yi Lin*
Affiliation:
Department of Mathematics, National Taiwan University, Taipei 106, Taiwan, Republic of China (d96221006@ntu.edu.tw)

Abstract

We develop a new non-vanishing theorem for del Pezzo surfaces with quotient singularities.

MSC classification

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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References

1. Belousov, G. N., Del Pezzo surfaces with log terminal singularities, Mat. Zametki 83(2) (2008), 170180 (in Russian).Google Scholar
2. Belousov, G., The maximal number of singular points on log del Pezzo surfaces, J. Math. Sci. Uni. Tokyo 16 (2009), 231238.Google Scholar
3. Cheltsov, I. and Shramov, C., Del Pezzo zoo, Exp. Math. 22(3) (2012), 313326.Google Scholar
4. Chen, J. A. and Chen, M., An optimal boundedness on weak ℚ-Fano threefolds, Adv. Math. 219 (2008), 20862104.CrossRefGoogle Scholar
5. Fulton, W., Introduction to toric varieties (Princeton University Press, Princeton, NJ, 1993).CrossRefGoogle Scholar
6. Hwang, D. and Keum, J., Algebraic Montgomery–Yang problem: the non-rational case, Mich. Math. J. 62 (1) (2013), DOI:10.1307/mmj/1363958239.Google Scholar
7. Kollár, J. and Mori, S., Birational geometry of algebraic varieties (Cambridge University Press, 1998).Google Scholar
8. Prokhorov, Y. G. and Verevkin, A. B., The Riemann–Roch theorem on surfaces with log-terminal singularities, J. Math. Sci. 140 (2) (2007), 200205.Google Scholar
9. Reid, M., Young person's guide to canonical singularities, Proc. Symp. Pure Math. 46 (1987), 343416.Google Scholar
10. M., Reid, Surface cyclic quotient singularities and Hirzebruch–Jung resolutions, Available at http://homepages.warwick.ac.uk/~masda/surf/more/cyclic.pdf (1997).Google Scholar
11. Shokurov, V. V., Complements on surfaces, J. Math. Sci. 102 (2) (2000), 38763932.CrossRefGoogle Scholar