相关论文: Special triple covers of algebraic surfaces

We give a description of the category of ordinary K3 surfaces over a finite field in terms of linear algebra data over Z. This gives an analogue for K3 surfaces of Deligne's description of the category of ordinary abelian varieties over a…

Let us consider the rank 14 lattice $P=D_4^3\oplus < -2> \oplus < 2>$. We define a K3 surface S of type P with the property that $P\subset {\rm Pic}(S) $, where ${\rm Pic}(S) $ indicates the Picard lattice of S. In this article we study the…

Let $k$ be an algebraically closed field of characteristic $p > 3$ and $S$ be a smooth projective surface over $k$ with $k$-rational point $x$. For $n \geq 2$, let $S^{[n]}$ denote the Hilbert scheme of $n$ points on $S$. In this note, we…

We discuss properties of the Seifert form for simple $K3$ singularities, and of the Picard lattices of families of weighted $K3$ surfaces. We study a collection $\mathcal{M}_{(\rho,\,\delta)}$ of $K3$ surfaces polarized by their Picard…

Given a polarized variety $(X,L)$, we construct and study projections of low degree $ X\dashrightarrow \mathbb{P}(H^0(L^\vee)) \dashrightarrow \mathbb P ^n $ using the associated kernel bundles. As an application, we can show that the…

In this paper we consider double covers of the projective space in relation with the problem of extensions of varieties, specifically of extensions of canonical curves to $K3$ surfaces and Fano 3-folds. In particular we consider $K3$…

We study the cohomological classification of vector bundles on smooth real affine surfaces and threefolds. We show that, as was observed in joint work in A. Asok and J. Fasel and in a coming joint paper with S. Banerjee and J. Fasel, under…

We compute divisors class groups of singular surfaces. Most notably we produce an exact sequence that relates the Cartier divisors and almost Cartier divisors of a surface to the those of its normalization. This generalizes Hartshorne's…

In this study, we construct four-dimensional F-theory models with 3 to 8 U(1) factors on products of K3 surfaces. We provide explicit Weierstrass equations of elliptic K3 surfaces with Mordell-Weil ranks of 3 to 8. We utilize the method of…

We prove that the Cuntz-Pimsner algebra O(E) of a vector bundle E over a compact metrizable space X is determined up to an isomorphism of C(X)-algebras by the ideal (1-[E])K(X) of the K-theory ring K(X). Moreover, if E and F are vector…

Answering a question posed by Enriques, we construct a minimal smooth algebraic surface $S$ of general type over the complex numbers with $K^2 = 45$ and $p_g = 4$, and with birational canonical map. Our surface is a regular (q=0) ball…

For a prime $p$, we study subgroups of order p of the Brauer group Br(S) of a general complex polarized K3 surface of degree 2d, generalizing earlier work of van Geemen. These groups correspond to sublattices of index p of the…

We survey crystalline cohomology, crystals, and formal group laws with an emphasis on geometry. We apply these concepts to K3 surfaces, and especially to supersingular K3 surfaces. In particular, we discuss stratifications of the moduli…

In this paper we determine the number of endomorphism rings of superspecial abelian surfaces over a field $\mathbb{F}_q$ of odd degree over $\mathbb{F}_p$ in the isogeny class corresponding to the Weil $q$-number $\pm\sqrt{q}$. This extends…

In this paper we study the cohomology of smooth projective complex surfaces $S$ of general type with invariants $p_g = q = 2$ and surjective Albanese morphism. We show that on a Hodge-theoretic level, the cohomology is described by the…

We introduce one of the most beautiful algebraic varieties known, a quintic hypersurface in projective five-space, which is invariant under the action of the Weyl group of $E_6$. This variety is intricately related with many other moduli…

We give a classification of rank $r$ torus equivariant vector bundles $\mathcal{E}$ on a toric scheme $\mathfrak{X}$ over a discrete valuation ring $\mathcal{O}$, in terms of graded piecewise linear maps $\Phi$ from the fan of…

This paper is the first in a series of three devoted to the smooth classification of simply connected elliptic surfaces. The method is to compute some coefficients of Donaldson polynomials of $SO(3)$ invariants whose second Stiefel-Whitney…

We study the orchard problem on cubic surfaces. We classify possibly reducible cubic surfaces $X\subseteq \mathbb{P}^3(\C)$ with smooth components on which there exist families of finite sets (of unbounded size) with quadratically many…

Let X be a Fano threefold, and let S be a K3 surface in X . Any moduli space M of simple vector bundles on S carries a holomorphic symplectic structure. Following an idea of Tyurin, we show that in some cases, those vector bundles which…