Boundedness of Fano Threefolds with Log-terminal Singularities of given Index
نویسندگان
چکیده
We prove that all Fano threefolds with log-terminal singularities of given index belong to finitely many families. This result was previously obtained by the author in the case of unipolar Fano varieties. [email protected]
منابع مشابه
Boundedness theorem for Fano log-threefolds
The main purpose of this article is to prove that the family of all Fano threefolds with log-terminal singularities with bounded index is bounded.
متن کاملBoundedness of Spherical Fano Varieties
Classically, G. Fano proved that the family of (smooth, anticanonically embedded) Fano 3-dimensional varieties is bounded, and moreover provided their classification, later completed by V.A. Iskovskikh, S. Mukai and S. Mori. For singular Fano varieties with log terminal singularities, there are two basic boundedness conjectures: Index Boundedness and the much stronger ǫ-lt Boundedness. The ǫ-lt...
متن کاملThe Cone of Effective Divisors of Log Varieties after Batyrev
In [Bat92] Batyrev studied the cone of pseudo-effective divisors on Q-factorial terminal threefolds and its dual cone, the cone of nef curves. Given a uniruled Q-factorial terminal threefold X , and an ample divisor H on X , he showed that the effective threshold of H (see Definition 1.5 below) is a rational number. Using similar arguments, Fujita generalized this result to log terminal pairs (...
متن کاملAn Optimal Boundedness on Weak Q-fano Threefolds
Let X be a terminal weak Q-Fano threefold. We prove that P −6(X) > 0 and P−8(X) > 1. We also prove that the anticanonical volume has a universal lower bound −K X ≥ 1/330. This lower bound is optimal.
متن کاملOn the Extendability of Projective Surfaces and a Genus Bound for Enriques-fano Threefolds
We introduce a new technique, based on Gaussian maps, to study the possibility, for a given surface, to lie on a threefold as a very ample divisor with given normal bundle. We give several applications, among which one to surfaces of general type and another one to Enriques surfaces. For the latter we prove that any threefold (with no assumption on its singularities) having as hyperplane sectio...
متن کامل