Related papers: Fields of definition of singular K3 surfaces

We discuss a notion of large complex structure for elliptic K3 surfaces with section inspired by the eight-dimensional F-theory/heterotic duality in string theory. This concept is naturally associated with the Type II Mumford partial…

We construct a simple finite-dimensional topological quantum field theory for compact 3-manifolds with triangulated boundary.

To a pair of elliptic curves, one can naturally attach two K3 surfaces: the Kummer surface of their product and a double cover of it, called the Inose surface. They have prominently featured in many interesting constructions in algebraic…

Using geometric engineering method of 4D $\mathcal{N}=2$ quiver gauge theories and results on the classification of Kac-Moody (KM) algebras, we show on explicit examples that there exist three sectors of $\mathcal{N}=2$ infrared CFT$_{4}$s.…

In this paper, we found non-symplectic index of all supersingular K3 surfaces defined over a field of characteristic p>3.

Let K be the function field of a smooth projective surface over a finite field. In this article, following the work of Parimala and Suresh, we establish a local-global principle for the divisibility of elements in H^3(K,Z/l) by elements in…

We give an elementary, self-contained and quick proof of Belyi's theorem. As a by-product of our proof we obtain an explicit bound for the degree of the defining number field of a Belyi surface.

We study the surface $\mathcal{W}_k : x^2 + y^2 + z^2 + x^2 y^2 z^2 = k x y z$ in $(\mathbb{P}^1)^3$, a tri-involutive K3 (TIK3) surface. We explain a phenomenon noticed by Fuchs, Litman, Silverman, and Tran: over a finite field of order…

Given an abelian surface, the number of its distinct decompositions into a product of elliptic curves has been described by Ma. Moreover, Ma himself classified the possible decompositions for abelian surfaces of Picard number $1 \leq \rho…

We verify that elliptic K3 surfaces and algebraic groups have many rational points over function fields, i.e., they are geometrically special in the sense of Javanpeykar-Rousseau. We also show that under additional assumptions, this…

An element in the Brauer group of a general complex projective $K3$ surface $S$ defines a sublattice of the transcendental lattice of $S$. We consider those elements of prime order for which this sublattice is Hodge-isometric to the…

The thesis deals with holomorphic germs $ \Phi: (\mathbb{C}^2, 0) \to (\mathbb{C}^3,0) $ singular only at the origin, with a special emphasis on the distinguished class of finitely determined germs. The results are published in two articles…

The moduli space of N=(4,4) string theories with a K3 target space is determined, establishing in particular that the discrete symmetry group is the full integral orthogonal group of an even unimodular lattice of signature (4,20). The…

We prove a formula for the polar degree of projective hypersurfaces in terms of the Milnor data of the singularities, extending to 1-dimensional singularities the Dimca-Papadima result for isolated singularities. We discuss the…

We construct a quasi-canonical lifting of a $K3$ surface of finite height over a finite field of characteristic $p\geq3$. Such results are previously obtained by Nygaard-Ogus when $p\geq5$. For this purpose, we use the display-theoretic…

Despite the transcendental nature of the twistor construction, the algebraic fibres of the twistor space of a K3 surface share certain arithmetic properties. We prove that for a polarized K3 surface with complex multiplication, all…

We investigate the universal Severi variety of rational curves on K3 surfaces, which parametrises irreducible rational curves in a fixed class on varying K3 surfaces of fixed genus. We investigate the conjecuted irreducibility of this space…

It was proved by Tien-Cuong Dinh and me that there is a smooth complex projective surface whose automorphism group is discrete and not finitely generated. In this paper, we will show that there is a smooth projective surface, birational to…

We generalize the spinorial characterization of isometric immersions of surfaces in R^3 given by T. Friedrich (On the spinor representation of surfaces in Euclidean 3-space, J. Geom. Phys. 28 (1998)) to surfaces in S^3 and H^3. The main…

We define an invariant, which we call surface-complexity, of compact 3-manifolds by means of Dehn surfaces. The surface-complexity is a natural number measuring how much the manifold is complicated. We prove that it fulfils interesting…