相关论文: Nef reduction and anticanonical bundles

In this paper, we prove the ampleness conjecture and Serrano's conjecture for strictly nef divisors on K-trivial fourfolds. Specifically, we show that any strictly nef divisors on projective fourfolds with trivial canonical bundle and…

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…

Consider a smooth projective 3-fold $X$ satisfying the Bogomolov-Gieseker conjecture of Bayer-Macr\`{i}-Toda (such as $\mathbb P^3$, the quintic threefold or an abelian threefold). Let $L$ be a line bundle supported on a very positive…

Let X be a smooth cubic threefold, M the moduli space of stable rank 2 vector bundles on X with trivial determinant and c_2=2 (the smallest value for which this space is non-empty). Recent results of Druel, Iliev, Markushevich and…

We give a $K$-theoretic criterion for a quasi-projective variety to be smooth. If $\mathbb{L}$ is a line bundle corresponding to an ample invertible sheaf on $X$, it suffices that $K_q(X) = K_q(\mathbb{L})$ for all $q\le\dim(X)+1$.

We present three interesting projective models of the supersingular K3 surface X in characteristic 5 with Artin invariant 1. For each projective model, we determine smooth rational curves on X with the minimal degree and the projective…

We prove that a geometrically integral smooth 3-fold $X$ with nef anti-canonical class and negative Kodaira dimension over a finite field $\mathbb{F}_q$ of characteristic $p>5$ and cardinality $q=p^e > 19$ has a rational point.…

The goal of this survey is to present various results concerning the cohomology of pseudoeffective line bundles on compact K{\"a}hler manifolds, and related properties of their multiplier ideal sheaves. In case the curvature is strictly…

We show the existence of a complex K3 surface $X$ which is not a Kummer surface and has a one-parameter family of Levi-flat hypersurfaces in which all the leaves are dense. We construct such $X$ by patching two open complex surfaces…

A smooth rational surface X is a Coble surface if the anti-canonical linear system is empty while the anti-bicanonical linear system is non-empty. In this note we shall classify these X and consider the finiteness problem of the number of…

On a threefold with trivial canonical bundle, Kuranishi theory gives an algebro-geometry construction of the (local analytic) Hilbert scheme of curves at a smooth holomorphic curve as a gradient scheme, that is, the zero-scheme of the…

Let X be a compact Kahler holomorphic-symplectic manifold, which is deformation equivalent to the Hilbert scheme of length n subschemes of a K3 surface. Let L be a nef line-bundle on X, such that the 2n-th power of c_1(L) vanishes and…

We study the geometry of the K3 surfaces $X$ with a finite number automorphisms and Picard number $\geq 3$. We describe these surfaces classified by Nikulin and Vinberg as double covers of simpler surfaces or embedded in a projective space.…

We study some foundational properties on discriminant divisors for generically smooth conic bundles. In particular, we extend the formula $\Delta_f \equiv -f_*K_{X/T}^2$ to arbitrary characteristics.

Let V be a smooth projective 3-fold of general type. Denote by $K^3$, a rational number, the self-intersection of the canonical sheaf of any minimal model of V. One defines $K^3$ as the canonical volume of $V$. Assume $p_g\ge 2$. We show…

We construct a non-Kummer projective K3 surface $X$ which admits compact Levi-flats by holomorphically patching two open complex surfaces obtained as the complements of tubular neighborhoods of elliptic curves embedded in blow-ups of the…

We give a cohomological classification of vector bundles of rank $2$ on a smooth affine threefold over an algebraically closed field having characteristic unequal to $2$. As a consequence we deduce that cancellation holds for rank $2$…

In this article, we investigate Serrano's conjecture for strictly nef divisors on projective bundles over higher dimensional smooth projective varieties.

We discuss N=2 supersymmetric compactifications to four dimensions from the point of view of F-theory and heterotic theory. In a relatively simple setup, we illustrate the spectral theory for vector bundles on K3xT^2 and discuss the…

We study the relation between semipositivity, nefness, and bigness of line bundles on compact K\"ahler manifolds. Every nef and big line bundle on a compact K\"ahler manifold $X$ is positive when ${\rm dim}\,X = 1$. Kim constructed an…