Curve Classes on Rationally Connected Varieties
We prove that every curve on a rationally connected variety is algebraically equivalent to a (non-effective) integral sum of rational curves.
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arXiv subjects
Hong R. Zong
Publications and source records attributed to Hong R. Zong.
On Rational Connectedness of Globally F-Regular Threefolds
In this paper, we show that projective globally $F$-regular threefolds, defined over an algebraically closed field of characteristic $p\geq 11$, are rationally chain connected.
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Weak Approximation for Isotrivial Families
We prove weak approximation for isotrivial families of rationally connected varieties defined over the function field of a smooth projective complex curve.
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On the Space of Conics on Complete Intersections
We get sharp degree bound for generic smoothness and connectedness of the space of conics in low degree complete intersections which generalizes the old work about Fano scheme of lines on Hypersurfaces.
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One Cycles on Rationally Connected Varieties
All curves on a separably rationally connected variety are rationally equivalent to a (non-effective) integral sum of rational curves, hence the first Chow group is generated by rational curves. Applying the same techniques, we also proved that the first Chow group of all separably rationally connected Fano complete intersections with index at least 2 is generated by lines. As a consequence, a question of Professor Burt Totaro about integral Hodge classess on rationally connected 3-folds is solved, and positive answer to the question for general n-fold due to Professor János Kollár will follow from the Tate conjecture for surfaces over finite fields.
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