Related papers: On numerically trivial automorphisms of threefolds…

Let $X$ be a minimal projective threefold of general type over $\mathbb{C}$ with only Gorenstein quotient singularities, and let $\mathrm{Aut}_{\mathbb{Q}}(X)$ be the subgroup of automorphisms acting trivially on $H^*(X,\mathbb{Q})$. In…

This thesis is devoted to the study of abelian automorphism groups of surfaces and $3$-folds of general type over complex number field $\Bbb C$. We obtain a linear bound in $K^3$ for abelian automorphism groups of $3$-folds of general type…

We prove that there exists a positive number $C_{n}$ depending only on $n$ such that for every smooth projective $n$-fold of general type $X$ defined over {\bf C}, the automorphism group $Aut(X)$ satisfies the inequality $\sharp{Aut}(X)\leq…

Let $\mathcal{X}$ be a smooth Fano threefold over the complex numbers of Picard rank $1$ with finite automorphism group. We give numerical restrictions on the order of the automorphism group $\mathrm{Aut}(\mathcal{X})$ provided the genus…

We give an effective upper bound of |Bir(X)| for the birational automorphism group of an irregular n-fold (with n = 3) of general type in terms of the volume V = V(X) under an ''albanese smoothness and simplicity'' condition. To be precise,…

It is known that the optimal Noether inequality $\mathrm{vol}(X) \ge \frac{4}{3}p_g(X) - \frac{10}{3}$ holds for every $3$-fold $X$ of general type with $p_g(X) \ge 11$. In this paper, we give a complete classification of $3$-folds $X$ of…

Let $S$ be a regular minimal surface of general type over the field of complex numbers, and $\mathrm{Aut}_\mathbb{Q}(S)$ the subgroup of automorphisms acting trivially on $H^*(S,\mathbb{Q})$. It has been known since twenty years that…

Let $X$ be a projective variety over an algebraically closed field $k$ of arbitrary characteristic $p \ge 0$. A surjective endomorphism $f$ of $X$ is $q$-polarized if $f^\ast H \sim qH$ for some ample Cartier divisor $H$ and integer $q >…

Let $X$ be a geometrically irreducible smooth projective curve, of genus at least three, defined over the field of real numbers. Let $G$ be a connected reductive affine algebraic group, defined over $\mathbb R$, such that $G$ is nonabelian…

Let $X$ be a variety of dimension $n$, and let $\mathrm{Aut}(X)$ be its automorphism group. When $X$ is quasi-affine, we prove that a solvable subgroup of $\mathrm{Aut}(X)$ that is generated by an irreducible family of automorphisms…

We generalize the equivariant intermediate Jacobian torsor obstruction over $\mathbb{C}$ to algebraically closed fields of characteristic zero. It is an obstruction to the (projective) linearizability problem of finite group actions on…

Let $X$ be a Gorenstein minimal projective $n$-fold with at worst locally factorial terminal singularities, and suppose that the canonical map of $X$ is generically finite onto its image. When $n<4$, the canonical degree is universally…

Let $X$ be a Gorenstein minimal $3$-fold of general type. We prove the optimal inequality: $$K_X^{3}\geq \frac{4}{3}\chi(\omega_X)-2,$$ where $\chi(\omega_X)$ is the Euler-Poincar$\acute{\text{e}}$ characteristic of the dualizing sheaf…

We prove that the degree of a nonconstant morphism from a smooth projective 3-fold $X$ with N\'{e}ron-Severi group ${\bf Z}$ to a smooth 3-dimensional quadric is bounded in terms of numerical invariants of $X$. In the special case where $X$…

Let $X$ be a smooth irregular $3$-fold of general type over $\mathbb{C}$. We prove that the optimal Noether inequality $$ \mathrm{vol}(X) \ge \frac{4}{3}p_g(X) $$ holds if $p_g(X) \ge 16$ or if $X$ has a Gorenstein minimal model. Moreover,…

Consider a smooth connected algebraic group $G$ acting on a normal projective variety $X$ with an open dense orbit. We show that Aut($X$) is a linear algebraic group if so is $G$; for an arbitrary $G$, the group of components of Aut($X$) is…

We prove two results about the natural representation of a group G of automorphisms of a normal projective threefold X on its second cohomology. We show that if X is minimal then G, modulo a normal subgroup of null entropy, is embedded as a…

1) We give a 3-dimensional analogue of M. Noether's inequality for canonically polarized threefolds: $K^3\ge 2(2p_g-5)/3$. This inequality is sharp by known examples of M. Kobayashi. 2) Given a minimal 3-fold $X$ of general type with…

Our main result is the determination of the respective groups $ Aut_\mathbb{Z}(S) $ of cohomologically trivial automorphisms and $ Aut_\mathbb{Q}(S) $ of numerically trivial automorphisms for the reducible fake quadrics, that is, the…

We prove: Let $G$ be a finite abelian group acting faithfully on a complex smooth project variety $X$ of general type with numerically effective canonical divisor, of dimension $n$. Then $$|G| \le C(n)K_X^n ,$$ where $C(n)$ depends only on…