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In this paper we study the algebraic ranks of foliations on Q-factorial normal projective varieties. We start by establishing a Kobayashi-Ochiai's theorem for Fano foliations in terms of algebraic ran...
The research on Fano variety is always a central topic in mathematics. In the recent years, there has been vast progress in the the problems on boundedness,stability and moduli space.The primary goal ...
In this paper we classify n-dimensional Fano manifolds with index >=n-2 and positive second Chern character.
Abstract: We prove a type of the Lefschetz hyperplane section theorem on Q-Fano 3-folds with Picard number one and $1/2(1,1,1)$-singularities by using some degeneration method. As a byproduct, we obta...
Abstract: Let (X,D) be a dlt pair, where X is a normal projective variety. Let S denote the support of the rounddown of D, and K the canonical divisor of X. We show that any smooth family of canonical...
Abstract: In this paper, we extend the method in [TZhu5] to study the energy level $L(\cdot)$ of Perelman's entropy $\lambda(\cdot)$ for K\"ahler-Ricci flow on a Fano manifold. Consequently, we first ...
Abstract: We show a relation between the birational superrigidity of Fano manifold and its slope stability in the sense of Ross-Thomas.
Abstract: We show that a Fano manifold (X,-K_X) is not slope stable with respect to a smooth curve Z if and only if (X,Z) is isomorphic to one of (projective space, line), (product of projective line ...
The symmetric projective varieties of rank one are all smooth and Fano by a classic result of Akhiezer. We classify the locally factorial (respectively smooth) projective symmetric G-varieties of rank...
Bernardi and Tirabassi show the existence of a full strong excep-tional collection consisting of line bundles on smooth toric Fano 3-folds under assuming Bondal’s conjecture, which states that the Fro...
This is a continuation of paper [7]. On any toric Fano manifold, we discuss the behavior of limit metric of a sequence of metrics, which are solutions to a continuity family of complex Monge-Amp`ere e...
G-Fano threefolds, I      G-Fano threefolds       2011/2/25
We classify Fano threefolds with only terminal sin-gularities whose canonical class is Cartier and divisible by 2, and satisfying an additional assumption that the G-invariant part of the Weil diviso...
The bidirectional Fano algorithm (BFA) can achieve at least two times decoding throughput compared to the conventional unidirectional Fano algorithm (UFA). In this paper, bidirectional Fano decoding i...
The aim of this work is to provide the first examples of $n$-dimensional varieties of wild representation type, for arbitrary $n\geq 2$. More precisely, we prove that all Fano blow-ups of $\PP^n$ at a...
We study the group of relative Fourier-Mukai transforms for Weierstrass fibrations, abelian schemes and Fano or anti-Fano fibrations. For Weierstrass and Fano or anti-Fano fibrations we are able to d...

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