Diller, Jeffrey Lin, Jan-Li
Published in
Mathematische Annalen

Let f:S⤏S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f:S\dashrightarrow S$$\end{document} be a rational self-map of a smooth complex projective surface S\documentcl...

Cerveau, Dominique Déserti, Julie
Published in
Forum Mathematicum

The Cremona group of birational transformations of ℙℂ2 acts on the space 𝔽(2) of holomorphic foliations on the complex projective plane. Since this action is not compatible with the natural graduation of 𝔽(2) by the degree, its description is complicated. The fixed points of the action are essentially described by Cantat and Favre in [J. Reine Ange...

Simis, Aron Tohǎneanu, Stefan O.
Published in
Collectanea Mathematica

We study the structure of the Rees algebra of almost complete intersection ideals of finite colength in low-dimensional polynomial rings over fields. The main tool is a mix of Sylvester forms and iterative mapping cone construction. The material developed spins around ideals of forms in two or three variables in the search of those classes for whic...

Trepalin, Andrey
Published in
Open Mathematics

Let $$\Bbbk$$ be a field of characteristic zero and G be a finite group of automorphisms of projective plane over $$\Bbbk$$. Castelnuovo’s criterion implies that the quotient of projective plane by G is rational if the field $$\Bbbk$$ is algebraically closed. In this paper we prove that $${{\mathbb{P}_\Bbbk ^2 } \mathord{\left/ {\vphantom {{\mathbb...

Bogomolov, Fedor Prokhorov, Yuri
Published in
Open Mathematics

We discuss the problem of stable conjugacy of finite subgroups of Cremona groups. We compute the stable birational invariant H 1(G, Pic(X)) for cyclic groups of prime order.

Bisi, Cinzia Calabri, Alberto Mella, Massimiliano
Published in
The Journal of Geometric Analysis

We study the quasi-projective variety \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\operatorname{Bir}_{d}$\end{document} of plane Cremona transformations defined by t...

Cutrone, Joseph Marshburn, Nicholas
Published in
Open Mathematics

In this paper, examples of type II Sarkisov links between smooth complex projective Fano threefolds with Picard number one are provided. To show examples of these links, we study smooth weak Fano threefolds X with Picard number two and with a divisorial extremal ray. We assume that the pluri-anticanonical morphism of X contracts only a finite numbe...

De Volder, Cindy Laface, Antonio
Published in
Journal of Pure and Applied Algebra

Let X be the blow-up of the three dimensional complex projective space along r points in very general position on a smooth elliptic quartic curve B⊂P3 and let L∈Pic(X) be any line bundle. The aim of this paper is to provide an explicit algorithm for determining the dimension of H0(X,L).

Avritzer, Dan Gonzalez-Sprinberg, Gerard Pan, Ivan
Published in
Rendiconti del Circolo Matematico di Palermo

Let X be a quadratic complex given by the intersection of two nonsingular quadrics in a projective space of dimension five. Let L be a line contained in X, and π the projection from X to a projective three space with center L. When X is nonsingular the map π is birational and the base locus scheme of π−1 is a smooth quintic curve of genus 2. Now as...

Sakovics, Dmitrijs
Published in
Open Mathematics

A singularity is said to be weakly-exceptional if it has a unique purely log terminal blow-up. In dimension 2, V. Shokurov proved that weakly-exceptional quotient singularities are exactly those of types D n, E 6, E 7, E 8. This paper classifies the weakly-exceptional quotient singularities in dimensions 3 and 4.