Related papers: Mori dream singular $K3$ surfaces

In this paper, we describe the Fourier-Mukai locus of the derived category of a complex algebraic K3 surface of Picard number one. We also prove that the Fourier-Mukai locus of the derived category of a complex algebraic K3 surface of…

Based on the result on derived categories on K3 surfaces due to Mukai and Orlov and the result concerning almost-prime numbers due to Iwaniec, we remark the following fact: For any given positive integer N, there are N (mutually…

Using results of our papers [19], [20] and [21] about classification of degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups, we classify Picard lattices of Kahlerian K3 surfaces. By classification we understand…

We establish a relationship between mirror symmetry for K3 surfaces and Arnold's strange duality for K3 surfaces. We compute various examples of mirror families. Among them the mirror moduli family for the moduli space of degree 2n…

In this paper we investigate two stratifications of the moduli space of elliptically fibred K3 surfaces. The first comes from Shimada's classification of connected components of elliptically fibred K3 surfaces and is closely related to the…

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 show that K3 surfaces in characteristic 2 can admit sets of $n$ disjoint smooth rational curves whose sum is divisible by 2 in the Picard group, for each $n=8,12,16,20$. More precisely, all values occur on supersingular K3 surfaces, with…

Let X be a K3 surface with a polarization H of degree H^2=2rs and with a primitive Mukai vector (r,H,s). The moduli space of sheaves over X with the isotropic Mukai vector (r,H,s) is again a K3 surface Y. We prove that Y\cong X, if Picard…

We study blowups of weighted projective planes at a general point, and more generally blowups of toric surfaces of Picard number one. Based on the positive characteristic methods of Kurano and Nishida, we give a general method for…

We investigate nef and movable cones of hypersurfaces in Mori dream spaces. The first result is: Let $Z$ be a smooth Mori dream space of dimension at least four whose extremal contractions are of fiber type of relative dimension at least…

Let X be a K3 surface of degree 8 in P^5 with hyperplane section H. We associate to it another K3 surface M which is a double cover of P^2 ramified on a sextic curve C. In the generic case when X is smooth and a complete intersection of…

General criteria are given for when an embedding of a Mori dream space into another satisfies certain nice combinatorial conditions on some of their associated cones. An explicit example of such an embedding is studied.

In this paper we prove some results about K3 surfaces with Picard number 1 and 2. In particular, we give a new simple proof of a theorem due to Oguiso which shows that, given an integer $N$, there is a K3 surface with Picard number 2 and at…

The goal of the present article is to survey the general theory of Mori Dream Spaces, with special regards to the question: When is the blow-up of toric variety at a general point a Mori Dream Space? We translate the question for toric…

We give construction of singular K3 surfaces with discriminant 3 and 4 as double coverings over the projective plane. Focusing on the similarities in their branching loci, we can generalize this construction, and obtain a three dimensional…

The aim of this paper is to describe algebraic K3 surfaces with an even set of rational curves or of nodes. Their minimal possible Picard number is nine. We completely classify these K3 surfaces and after a carefull analysis of the divisors…

We determine the Mori cone of holomorphic symplectic varieties deformation equivalent to the punctual Hilbert scheme on a K3 surface. Our description is given in terms of Markman's extended Hodge lattice.

Consider the blow-up $X$ of $\mathbb{P}^3$ at 6 points in very general position and the 15 lines through the 6 points. We construct an infinite-order pseudo-automorphism $\phi_X$ on $X$, induced by the complete linear system of a divisor of…

Given a K3 surface X over a field of characteristic p, Artin conjectured that if X is supersingular (meaning infinite height) then its Picard rank is 22. Along with work of Nygaard-Ogus, this conjecture implies the Tate conjecture for K3…

Nikulin and Vinberg proved that there are only a finite number of lattices of rank $\geq 3$ that are the N\'eron-Severi group of projective K3 surfaces with a finite automorphism group. The aim of this paper is to provide a more geometric…