Wehlau, David L.
Published in
Forum Mathematicum

We consider a Weitzenböck derivation Δ acting on a polynomial ring R=K[ξ 1 ,ξ 2 ,...,ξ m ]$ R=K[\xi _1,\xi _2,\ldots ,\xi _m] $ over a field K of characteristic 0. The K-algebra R Δ ={h∈R∣Δ(h)=0}${R^\Delta = \lbrace h \in R \mid \Delta (h) = 0\rbrace }$ is called the algebra of constants. Nowicki considered the case where the Jordan matrix for Δ ac...

Lamy, Stéphane Sebag, Julien

Let X be a smooth projective complex variety, of dimension 3, whose Hodge numbers h^{3,0}(X), h^{1,0}(X) both vanish. Let f: X--> X be a birational map that induces an isomorphism on (dense) open subvarieties U,V of X. Then we show that the complex reduced varieties (X \ U), (X \ V) are piecewise isomorphic.

Chaput, Pierre-Emmanuel Sabatino, Pietro
Published in
Collectanea Mathematica

In this paper we consider homaloidal polynomial functions f such that their multiplicative Legendre transform f*, defined as in Etingof et al. (Sel. Math. (N.S.) 8(1):27–66, 2002), Section 3.2 is again polynomial. Following Dolgachev (Michigan Math. J. 48:191–202, 2000), we call such polynomials EKP-homaloidal. We prove that every EKP-homaloidal po...

Doria, A.V. Hassanzadeh, S.H. Simis, A.
Published in
Advances in Mathematics

One develops ab initio the theory of rational/birational maps over reduced, but not necessarily irreducible, projective varieties in arbitrary characteristic. A virtual numerical invariant of a rational map is introduced, called the Jacobian dual rank. It is proved that a rational map in this general setup is birational if and only if the Jacobian ...

Rabanal, Roland
Published in
Bulletin of the Brazilian Mathematical Society, New Series

F: ℝ2 → ℝ2 is an almost-area-preserving map if: (a) F is a topological embedding, not necessarily surjective; and (b) there exists a constant s > 0 such that for every measurable set B, µ(F(B)) = sµ(B) where µ is the Lebesgue measure. We study when a differentiable map whose Jacobian determinant is nonzero constant to be an almost-area-preserving m...

Huisman, Johannes Mangolte, Frédéric
Published in
manuscripta mathematica

Let X be a singular real rational surface obtained from a smooth real rational surface by performing weighted blow-ups. Denote by Aut(X) the group of algebraic automorphisms of X into itself. Let n be a natural integer and let e = [e1, . . . , eℓ] be a partition of n. Denote by Xe the set of ℓ-tuples (P1, . . . , Pℓ) of disjoint nonsingular curvili...

Iwasaki, Katsunori Uehara, Takato
Published in
Mathematische Zeitschrift

It is a basic problem to count the number of periodic points of a surface mapping, since the growth rate of this number as the period tends to infinity is an important dynamical invariant. However, this problem becomes difficult when the map admits curves of periodic points. In this situation we give a precise estimate of the number of isolated per...

Cheltsov, Ivan Park, Jihun
Published in
Open Mathematics

On a general quasismooth well-formed weighted hypersurface of degree Σi=14 a i in ℙ(1, a 1, a 2, a 3, a 4), we classify all pencils whose general members are surfaces of Kodaira dimension zero.

Tsuda, Teruhisa Takenawa, Tomoyuki
Published in
Advances in Mathematics

Starting from certain rational varieties blown-up from ( P 1 ) N , we construct a tropical, i.e., subtraction-free birational, representation of Weyl groups as a group of pseudo-isomorphisms of the varieties. We develop an algebro-geometric framework of τ-functions as defining functions of exceptional divisors on the varieties. In the case where th...

Cheltsov, Ivan
Published in
Geometric and Functional Analysis

We study global log canonical thresholds of del Pezzo surfaces. All varieties are assumed to be defined over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{C}...