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Invertible cohomological field theories and Weil-Petersson volumes

Yuri I. Manin, Peter Zograf (2000)

Annales de l'institut Fourier

We show that the generating function for the higher Weil–Petersson volumes of the moduli spaces of stable curves with marked points can be obtained from Witten’s free energy by a change of variables given by Schur polynomials. Since this generating function has a natural extension to the moduli space of invertible Cohomological Field Theories, this suggests the existence of a “very large phase space”, correlation functions on which include Hodge integrals studied by C. Faber and R. Pandharipande....

Invertible polynomial mappings via Newton non-degeneracy

Ying Chen, Luis Renato G. Dias, Kiyoshi Takeuchi, Mihai Tibăr (2014)

Annales de l’institut Fourier

We prove a sufficient condition for the Jacobian problem in the setting of real, complex and mixed polynomial mappings. This follows from the study of the bifurcation locus of a mapping subject to a new Newton non-degeneracy condition.

Involutive birational transformations of arbitrary complexity in Euclidean spaces

Zdeněk Dušek, Oldřich Kowalski (2013)

Commentationes Mathematicae Universitatis Carolinae

A broad family of involutive birational transformations of an open dense subset of n onto itself is constructed explicitly. Examples with arbitrarily high complexity are presented. Construction of birational transformations such that φ k = Id for a fixed integer k > 2 is also presented.

Irreducible algebraic sets of matrices with dominant restriction of the characteristic map

Marcin Skrzyński (2003)

Mathematica Bohemica

We collect certain useful lemmas concerning the characteristic map, 𝒢 L n -invariant sets of matrices, and the relative codimension. We provide a characterization of rank varieties in terms of the characteristic map as well as some necessary and some sufficient conditions for linear subspaces to allow the dominant restriction of the characteristic map.

Is the Luna stratification intrinsic?

Jochen Kuttler, Zinovy Reichstein (2008)

Annales de l’institut Fourier

Let G GL ( V ) be a representation of a reductive linear algebraic group G on a finite-dimensional vector space V , defined over an algebraically closed field of characteristic zero. The categorical quotient X = V // G carries a natural stratification, due to D. Luna. This paper addresses the following questions:(i) Is the Luna stratification of X intrinsic? That is, does every automorphism of V // G map each stratum to another stratum?(ii) Are the individual Luna strata in X intrinsic? That is, does every automorphism...

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