Related papers: An inequality for adjoint rational surfaces

We study the dominant rational maps from a general surface in P^{3} to surfaces of general type. We prove restrictions on the target surfaces, and special properties of the rational maps. We show that for a small degree the general surface…

We introduce the problem of partitioning 2D regions (usually convex regions) into mutually congruent pieces ('tiles').

The main geometric result of this paper is that given any family of surfaces of general type f:X-->B, for sufficiently large n the fiber product X^n_B dominates a variety of general type. This result is especially interesting when it is…

In this paper we prove new lower bounds for the minimum distance of a toric surface code defined by a convex lattice polygon P. The bounds involve a geometric invariant L(P), called the full Minkowski length of P which can be easily…

Some inequalities for positive linear maps on matrix algebras are given, especially asymmetric extensions of Kadison's inequality and several operator versions of Chebyshev's inequality. We also discuss well-known results around the matrix…

We study some properties convex functions fulfill. Among the conclusions we obtain from such result, we are able to prove some nontrivial inequalities among real numbers, and we give an improvement of the reverse triangle inequality in the…

Optical surfaces represented by second-degree polynomials (quadratic or conics) are ubiquitous in optics. We revisit the equations of the conic shapes in the context of grazing incidence optics, gathering together the curves commonly used…

We present a generalization of the Bogomolov-Miyaoka-Yau inequality to Deligne-Mumford surfaces of general type.

This is a survey of the geometry of complex cubic fourfolds with a view toward rationality questions. Topics include classical constructions of rational examples, Hodge structures and special cubic fourfolds, associated K3 surfaces and…

We prove a Diophantine approximation inequality for closed subschemes on surfaces which can be viewed as a joint generalization of recent inequalities of Ru-Vojta and Heier-Levin in this context. As applications, we study various…

We give in this article necessary and sufficient conditions on the topology of rationally and polynomially convex domains.

We study the multi-height distribution of rational points of smooth, projective and split toric varieties over $\mathbf{Q}$ using the lift of the number of points to universal torsors.

In this note, we derive an asymptotically sharp upper bound on the number of lattice points in terms of the volume of centrally symmetric convex bodies. Our main tool is a generalization of a result of Davenport that bounds the number of…

Problems related to projections on closed convex cones are frequently encountered in optimization theory and related fields. To study these problems, various unifying ideas have been introduced, including asymmetric vector-valued norms and…

We give cohomological criteria for logarithmic good reduction of elliptic surfaces up to modification. Along the way, we prove several more general results about such surfaces in positive characteristic, as well as about log smooth…

First, we examine the notion of nonrational convex polytope and nonrational fan in the context of toric geometry. We then discuss and interrelate some recent developments in the subject.

Majorization inequalities for symmetric polynomials have interested mathematicians for centuries, from the AM-GM inequality for two variables going back at least to Euclid, through classical results of Newton, Muirhead and Gantmacher, to…

We study the distribution of algebraic points on K3 surfaces.

We show that the counting of rational curves on a complete toric variety that are in general position to the toric prime divisors coincides with the counting of certain tropical curves. The proof is algebraic-geometric and relies on…

This memoir is devoted to the study of formal-analytic arithmetic surfaces. These are arithmetic counterparts, in the context of Arakelov geometry, of germs of smooth complex-analytic surfaces along a projective complex curve.…