The aim of the present paper is to provide an intrinsic investigation of projective changes in Finlser geometry, following the pullback formalism. Various known local results are generalized and other new intrinsic results are obtained. Nontrivial characterizations of projective changes are given. The fundamental projectively invariant tensors, namely, the projective deviation tensor, the Weyl ...

The goal of this paper is to present a modified version (GML) of ML invariant which should take into account rulings over a projective base and allow further stratification of smooth affine rational surfaces. We provide a non-trivial example where GML invariant is computed for a smooth affine rational surface admitting no C-actions. We apply GML invariant to computing ML invariant of some three...

In this paper, some fundamental limitations of projective invariants of non-algebraic planar curves are discussed. It is shown that all curves within a large class can be mapped arbitrarily close to a circle by projective transformations. It is also shown that arbitrarily close to each of a finite number of closed planar curves there is one member of a set of projectively equivalent curves. Thu...

After Bershadsky-Cecotti-Ooguri-Vafa, we introduce an invariant of Calabi-Yau threefolds, which we call the BCOV invariant and which we obtain using analytic torsion. We give an explicit formula for the BCOV invariant as a function on the compactified moduli space, when it is isomorphic to a projective line. As a corollary, we prove the formula for the BCOV invariant of quintic mirror threefold...

This work concerns the problem of relating characteristic numbers of onedimensional holomorphic foliations of PC to those of algebraic varieties invariant by them. More precisely: if M is a connected complex manifold, a one-dimensional holomorphic foliation F of M is a morphism Φ : L −→ TM where L is a holomorphic line bundle on M . The singular set of F is the analytic subvariety sing(F) = {p ...

We prove that a rational linear combination of Chern numbers is an oriented diffeomorphism invariant of smooth complex projective varieties if and only if it is a linear combination of the Euler and Pontryagin numbers. In dimension at least three we prove that only multiples of the top Chern number, which is the Euler characteristic, are invariant under diffeomorphisms that are not necessarily ...

This paper presents an algorithm for using projective invariant patterns in augmented reality applications. It is actually an adaptation of a previous algorithm for an optical tracking device, that works with infrared illumination and filtering. The present algorithm removes the necessity of working in a controlled environment, which would be inadequate for augmented reality applications. In or...

We define projective GIT quotients, and introduce toric varieties from this perspective. We illustrate the definitions by exploring the relationship between toric varieties and polyhedra. Geometric invariant theory (GIT) is a theory of quotients in the category of algebraic varieties. Let X be a projective variety with ample line bundle L, and G an algebraic group acting on X, along with a lift...

We introduce the class of projective reflection groups which includes all complex reflection groups. We show that several aspects involving the combinatorics and the representation theory of complex reflection groups find a natural description in this wider setting. Résumé. On introduit la classe des groupes de réflexions projectifs, ce qui généralises la notion de groupe engendré par des réfle...