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On the geography of threefolds of general type

Authors:	Jungkai A Chen Christopher D Hacon

Institution:	1. Taida Institute for Mathematical Sciences, National Center for Theoretical Sciences, Taipei Office, National Taiwan University, Taipei, 106, Taiwan;2. Department of Mathematics, National Taiwan University, Taipei, 106, Taiwan;3. Department of Mathematics, University of Utah, 155 South 1400 East, Room 233 Salt Lake City, UT 84112, USA

Abstract:	Let X be a complex nonsingular projective 3-fold of general type. We show that there are positive constants c, $c^{'}$ and $m_{1}$ such that $χ (ω_{X}) ? ? c Vol (X)$ and $P_{m} (X) ? c^{'} m^{3} Vol (X)$ for all $m ? m_{1}$ .

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