相关论文: Luigi Cremona and cubic surfaces

Giovanni Battista Benedetti (1530--1590) derived two constructions of ovals given their minor and major axes. These were published in 1585 and seem to be the first solution to this problem. Therefore, the generally accepted view that ``the…

In this paper, we give a survey of a geometrical theory of Jacobi forms of higher degree. And we present some geometric results and discuss some geometric problems to be investigated in the future.

We give an elementary introduction to the theory of supermembranes.

This entry reviews Rudolf Carnap's philosophical views on the quantum mechanics of his time. It also offers some thoughts on how Carnap might have reacted to some recent developments in the foundations of quantum mechanics.

We classify all possible automorphism groups of smooth cubic surfaces over an algebraically closed field of arbitrary characteristic. As an intermediate step we also classify automorphism groups of quartic del Pezzo surfaces. We show that…

We show that the hessian map of quartic plane curves is a birational morphism onto its image, thus bringing new evidence for a very interesting conjecture of Ciro Ciliberto and Giorgio Ottaviani. Our new approach also yields a simpler proof…

These notes outline some basic notions of Tropical Geometry and survey some of its applications for problems in classical (real and complex) geometry. To appear in the Proceedings of the Madrid ICM.

We consider the Zariski-Lipman Conjecture on free module of derivations for algebraic surfaces. Using the theory of non-complete algebraic surfaces, and some basic results about ruled surfaces, we will prove the conjecture for several…

This is a brief account of my results with George Boxer, Frank Calegari and Vincent Pilloni on the (potential) modularity of abelian surfaces.

We study the geometry and codes of quartic surfaces with many cusps. We apply Gr\"obner bases to find examples of various configurations of cusps on quartics.

Segre proved that a smooth cubic surface over Q is unirational iff it has a rational point. We prove that the result also holds for cubic hypersurfaces over any field, including finite fields.

We will try to give an overview of one of the landmark results of Jorge Lewowicz: his classification of expansive homeomorphisms of surfaces. The goal will be to present the main ideas with the hope of giving evidence of the deep and…

The notions of discrete conformality on triangle meshes have rich mathematical theories and wide applications. The related notions of discrete uniformizations on triangle meshes, suggest efficient methods for computing the uniformizations…

The goal of this paper is to prove Bloch's conjecture for the numerical Godeaux surface constructed by P. Craighero and R. Gattazzo.

This is a note constructing a certain weight 4 automorphic form on the moduli space of cubic surfaces, posted here because it is referred to in math.AG/0002066

We establish Manin's conjecture for a cubic surface split over Q and whose singularity type is 2A_2+A_1. For this, we make use of a deep result about the equidistribution of the values of a certain restricted divisor function in three…

We present a study of cubic surfaces from the novel perspective of positive geometry. Our positive geometries have dimension two (the surface minus its 27 lines), dimension three (its complement in 3-space), and dimension four (the moduli…

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…

The question of the distribution of shapes of unit lattices in number fields, pioneered by Margulis and Gromov, has lately attracted considerable interest, not least because of the lack of available results. Here we prove that the set of…

Introductory lectures notes on cosmology, aimed at master students in physics and based on a course held at Milano University (in Italian).