Rational connectedness of log Q-Fano varieties

By Qi S. Zhang. 2004

141 citations recorded by the source corpus.

Abstract In this paper, we give an affirmative answer to a conjecture in the Minimal Model Program. We prove that log Q-Fano varieties are rationally connected. We also study the behavior of the canonical bundles under projective morphisms.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7aa14e33b998d6f73f0a2985df059b73d56740e0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. C. Birkar
2. Chi Li
3. Yuri Prokhorov
4. Sheng Meng
5. De-Qi Zhang
6. Hiromu Tanaka
7. Y. Odaka
8. H. Blum

In Mathematical Physics

1. C. Birkar
2. Sheng Meng
3. De-Qi Zhang
4. Chi Li
5. Yuri Prokhorov
6. Hiromu Tanaka
7. K. A. Shramov
8. Ivan Cheltsov

Citations in the corpus

• Behavior of canonical divisors under purely inseparable base changes (2015, background): “w that BEHAVIOR OF CANONICAL DIVISORS 5 every smooth Fano variety, defined over an algebraically closed field of any characteristic, is rationally chain connected. After that, Hacon– McKernan ([8]) and [22] prove that log Fano varieties in characteristic zero are rationally connected. In positive char”
• Building blocks of polarized endomorphisms of normal projective varieties (2016, background): “Clearly, Xr−1 is then a Fano variety of Picard number one, so Xr−1 and hence X are rationally connected; see [38].”
• Simple finite subgroups of the Cremona group of rank 3 (2009, background): “According to [Zha06] Fano varieties with log terminal singularities are rationally connected, so our constructions give embeddings of a finite simple group into the automorphism group of some rationally connected variety.”
• LOG CANONICAL THRESHOLDS OF SMOOTH FANO THREEFOLDS (2008, background): “The group Pic(X) is torsion free, because X is rationally connected (see [4]).”
• Special test configurations and $K$-stability of Fano varieties (2011, methodology): “tional image of such E 1. As investigated in [Kol07a, HX09], the component E 1 constructed in this way has many interesting geometric properties. Since any Q-Fano variety is rationally connected (see [Zha06]), the argument which we just presented indeed gives a new proof of [HX09, Theorem 3.1] which”
• Anti-pluricanonical systems on Fano varieties (2016, background): “Since X ′ is of Fano type, the general fibres of f ′ are also of Fano type, hence they are rationally connected which in turn implies the general fibres of f are rationally connected [16][46].”