Related papers: Luigi Cremona and cubic surfaces

We discuss the work of Corrado Segre on nodal cubic hypersurfaces with emphasis on the cases of 6-nodal and 10-nodal cubics. In particular, we discuss the Fano surface of lines and conic bundle structures on such threefolds. We review some…

Naruki gave an explicit construction of the moduli space of marked cubic surfaces, starting from a toric variety and proceeding with blow ups and contractions. Using his result, we compute the Chow groups and the Chern classes of this…

This article gives a conceptual introduction to the topos approach to the formulation of physical theories.

Previous work of the author has developed coordinates on bundles over the classical Teichmueller spaces of punctured surfaces and on the space of cosets of the Moebius group in the group of orientation-preserving homeomorphisms of the…

Alain Connes introduced the use of Lie groupoids in noncommutative geometry in his pioneering work on the index theory of foliations. In the present paper, we recall the basic notion involved: groupoids, their C*-algebras, their…

We give a geometric approach to the proof of the $\lambda$-lemma. In particular, we point out the role pseudoconvexity plays in the proof.

We apply our earlier results on Fourier-Mukai partners to answer definitively a question about Kummer surface structures, posed by T. Shioda 25 years ago.

Building blocks and tiles are an excellent way of learning about geometry and mathematics in general. There are several versions of tiles that are either snapped together or connected with magnets that can be used to introduce topics like…

We report on our project to construct non-singular cubic surfaces over $\bbQ$ with a rational line. Our method is to start with degree 4 Del Pezzo surfaces in diagonal form. For these, we develop an explicit version of Galois descent.

For each closed orientable surface we introduce a simplical complex with some additional structure which is a version of the complex of curves of this surface adjusted to investigation of its Torelli group. We call this complex the Torelli…

We discuss quantum analogues of minimal surfaces in Euclidean spaces and tori.

The goal of these notes is to provide an informal introduction to Gromov-Witten theory with an emphasis on its role in counting curves in surfaces. These notes are based on a talk given at the Fields Institute during a week-long conference…

An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…

Traves and Wehlau recently gave a straightedge construction that checks whether 10 points lie on a plane cubic curve. They also highlighted several open problems in the synthetic geometry of cubics. Hermann Grassmann investigated incidence…

One applies the symmetry group theory for study the partial differential equations of Tzitzeica surfaces theory. One finds infinitesimal symmetries, Lagrangians and a new solution of Titzeica equation.

This article shows that the Cremona group is compactly presentable. To prove this we show that it is a generalised amalgamated product of three of its algebraic subgroups (automorphisms of the plane and Hirzebruch surfaces) divided by one…

Galileo's support to the Copernican theory was decisive for the revolutionary astronomical discoveries he achieved in 1610. We trace the origins of Galileo's conversion to the Copernican theory, discussing in particular the "Dialogo de…

We extend our classification of special Cremona transformations whose base locus has dimension at most three to the case when the target space is replaced by a (locally) factorial complete intersection.

The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be…

We construct nontrivial homomorphisms from the quasi group of some cubic surfaces over $\bbF_{\!p}$ into a group. We show experimentally that the homomorphisms constructed are the only possible ones and that there are no nontrivial…