منابع مشابه
Rational Connectedness of Log Q-fano Varieties
Let X be a log Q-Fano variety, i.e, there exists an effective Q-divisor D such that (X,D) is Kawamata log terminal (klt) and −(KX + D) is nef and big. By a result of Miyaoka-Mori [15], X is uniruled. The conjecture ([10], [16]) predicts that X is rationally connected. In this paper, apply the theory of weak (semi) positivity of (log) relative dualizing sheaves f∗(KX/Y + ∆) (which has been devel...
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We prove that every globally F -regular variety is log Fano. In other words, if a prime characteristic variety X is globally F -regular, then it admits an effective Qdivisor ∆ such that −KX −∆ is ample and (X, ∆) has controlled (Kawamata log terminal, in fact globally F -regular) singularities. A weak form of this result can be viewed as a prime characteristic analog of de Fernex and Hacon’s ne...
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This note is an extension of the paper [HMP]. The main theorem of [HMP] states that a relatively smooth hypersurface (i.e. a hypersurface whose singular locus has sufficient large codimension with respect to its degree) is unirational. A mild modification can generalize this to complete intersections. As an application, we will show the Fano variety of a relatively smooth hypersurface is also u...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2015
ISSN: 0001-8708
DOI: 10.1016/j.aim.2015.08.001