Glazer, Itay Hendel, Yotam I.
Published in
Selecta Mathematica

Let K be a field of characteristic zero, X and Y be smooth K-varieties, and let V be a finite dimensional K-vector space. For two algebraic morphisms φ:X→V\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsi...

Campesato, Jean-Baptiste
Published in
Mathematische Zeitschrift

It has been recently proved that the arc-analytic type of a singular Brieskorn polynomial determines its exponents. This last result may be seen as a real analogue of a theorem by Yoshinaga and Suzuki concerning the topological type of complex Brieskorn polynomials. In the real setting it is natural to investigate further by asking how the signs of...

Ishii, Shihoko
Published in
European Journal of Mathematics

We study singularities in arbitrary characteristic. We propose finite determination conjecture for Mather–Jacobian minimal log discrepancies in terms of jet schemes of a singularity. The conjecture is equivalent to the boundedness of the number of the blow-ups to obtain a prime divisor which computes the Mather–Jacobian minimal log discrepancy. We ...

Lê, Quy Thuong
Published in
Vietnam Journal of Mathematics

We compute the motivic Milnor fiber of a complex plane curve singularity in an inductive and combinatoric way using the extended simplified resolution graph. The method introduced in this article has a consequence that one can study the Hodge–Steenbrink spectrum of such a singularity in terms of that of a quasi-homogeneous singularity.

Sebag, Julien
Published in
Archiv der Mathematik

Let k be a field of characteristic zero. Let V be a k-scheme of finite type, i.e., a k-variety, which is integral. We prove that if the associated arc scheme L∞(V)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlengt...

Thuong, Lê Quy
Published in
Acta Mathematica Vietnamica

In Kontsevich-Soibelman’s theory of motivic Donaldson-Thomas invariants for 3-dimensional noncommutative Calabi-Yau varieties, the integral identity conjecture plays a crucial role as it involves the existence of these invariants. A purpose of this note is to show how the conjecture arises. Because of the integral identity’s nature, we shall give a...

Ivorra, Florian Sebag, Julien
Published in
Selecta Mathematica

We prove that the construction of motivic nearby cycles, introduced by Jan Denef and François Loeser, is compatible with the formalism of nearby motives, developed by Joseph Ayoub. Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepack...

Bories, Bart
Published in
Revista Matemática Complutense

For a nonzero ideal \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {I}\lhd \mathbf {C}[x_{1},\ldots,x_{n}]$\end{document}, with \documentclass[12pt]{minimal} \...

de Fernex, Tommaso
Published in
Inventiones mathematicae

We prove that for N≥4, all smooth hypersurfaces of degree N in ℙN are birationally superrigid. First discovered in the case N=4 by Iskovskikh and Manin in a work that started this whole direction of research, this property was later conjectured to hold in general by Pukhlikov. The proof relies on the method of maximal singularities in combination w...

Mourtada, Hussein

For $m\in \mathbb{N}, m\geq 1,$ we determine the irreducible components of the $m-th$ jet scheme of a normal toric surface $S.$ We give formulas for the number of these components and their dimensions. When $m$ varies, these components give rise to projective systems, to which we associate a weighted graph. We prove that the data of this graph is e...