Results 41 to 50 of about 7,542 (104)

Generic root counts and flatness in tropical geometry

Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.
Abstract We use tropical and nonarchimedean geometry to study the generic number of solutions of families of polynomial equations over a parameter space Y$Y$. In particular, we are interested in the choices of parameters for which the generic root count is attained.
Paul Alexander Helminck, Yue Ren
wiley   +1 more source

Relative birational automorphisms of algebraic fiber spaces

Duke Mathematical Journal, 1991
The author continues his study of the scheme of birational automorphisms \(\hbox{Bir}(X)\) of a projective variety over an algebraically closed field of characteristic 0 [Compos. Math. 63, 123-142 (1987; Zbl 0655.14007) and Invent. Math. 93, No. 2, 383-403 (1988; Zbl 0661.14010)].
openaire   +2 more sources

On the inertia group of elliptic curves in the Cremona group of the plane

, 2007
We study the group of birational transformations of the plane that fix (each point of) a curve of geometric genus 1. A precise description of the finite elements is given; it is shown in particular that the order is at most 6, and that if the group ...
Blanc, Jérémy
core   +3 more sources

Arithmetic Satake compactifications and algebraic Drinfeld modular forms

Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.
Abstract In this article, we construct the arithmetic Satake compactification of the Drinfeld moduli schemes of arbitrary rank over the ring of integers of any global function field away from the level structure, and show that the universal family extends uniquely to a generalized Drinfeld module over the compactification.
Urs Hartl, Chia‐Fu Yu
wiley   +1 more source

Structure of birational automorphism groups, I: non-uniruled varieties

Inventiones Mathematicae, 1988
In a previous paper [Compos. Math. 63, 123-142 (1987; Zbl 0655.14007)] the author introduced the notion of the scheme of birational automorphisms Bir(X) of an algebraic variety X. In good cases (B-good) \(Bir(X)_{red}\) is a group scheme which acts birationally on some model of X, and is universal among such group schemes.
openaire   +1 more source

Non-rationality of some fibrations associated to Klein surfaces

, 2013
We study the polynomial fibration induced by the equation of the Klein surfaces obtained as quotient of finite linear groups of automorphisms of the plane; this surfaces are of type A, D, E, corresponding to their singularities.
A Premet, G Freudenburg, J Blanc, V Futorny, Yu Manin   +4 more
core   +1 more source

Relative and absolute Lefschetz standard conjectures for some Lagrangian fibrations

Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.
Abstract We show that the hyper‐Kähler varieties of OG10‐type constructed by Laza–Saccà–Voisin (LSV) verify the Lefschetz standard conjecture. This is an application of a more general result, stating that certain Lagrangian fibrations verify this conjecture. The main technical assumption of this general result is that the Lagrangian fibration satisfies
Giuseppe Ancona, Mattia Cavicchi, Robert Laterveer, Giulia Saccà   +3 more
wiley   +1 more source

Birational Automorphism Groups of Projective Varieties of Picard Number Two [PDF]

, 2014
title slightly changed to this; some proof simplified; submitted to the Proceedings of Groups of Automorphisms in Birational and Affine Geometry, 28 October - 3 November 2012, C.I.R.M., Trento ...
openaire   +2 more sources

Normal subgroups in the Cremona group (long version)

, 2012
Let k be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane P^2 over k is not a simple group.
D Osin, G Halphèn, G Higman, HWE Jung, I Chiswell, IV Dolgachev, IV Dolgachev, IV Dolgachev, J Blanc, J Blanc, J Diller, J Déserti, J Déserti, J Kollár, J-P Furter, JH Hubbard, M Ershov, R Lazarsfeld, RC Lyndon, S Boucksom, S Cantat, S Cantat, S Lamy, Serge Cantat, Stéphane Lamy, T Delzant, V Chaynikov, Yves Cornulier   +27 more
core   +3 more sources

Some applications of canonical metrics to Landau–Ginzburg models

Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.
Abstract It is known that a given smooth del Pezzo surface or Fano threefold X$X$ admits a choice of log Calabi–Yau compactified mirror toric Landau–Ginzburg model (with respect to certain fixed Kähler classes and Gorenstein toric degenerations).
Jacopo Stoppa
wiley   +1 more source