SINGULAR RATIONALLY CONNECTED THREEFOLDS WITH NON-ZERO PLURI-FORMS
This paper is concerned with singular projective rationally connected threefolds $X$ which carry non-zero pluri-forms, that is the reflexive hull of $({\rm\Omega}_{X}^{1})^{\otimes m}$ has a non-zero global section for some positive integer $m$. If $X$ has $\mathbb{Q}$-factorial terminal singularities, then we show that there is a fibration $p$ from $X$ to $\mathbb{P}^{1}$. Moreover, we give a formula for the numbers of $m$-pluri-forms as a function of the ramification of the fibration $p$.
2013 ◽
Vol 1
(2)
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pp. 177-191
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2009 ◽
Vol 52
(2)
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pp. 267-272
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2020 ◽
Vol 63
(4)
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pp. 1031-1047
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