Results 71 to 80 of about 555 (183)

The versal deformation of small resolutions of conic bundles over P1×P1${\mathbb {P}}^1\times {\mathbb {P}}^1$ with two sections blown down

Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.
Abstract Twistor spaces are certain compact complex three‐folds with an additional real fibre bundle structure. We focus here on twistor spaces over P2#P2#P2${\mathbb {P}}^2\#{\mathbb {P}}^2\#{\mathbb {P}}^2$. Such spaces are either small resolutions of double solids or they can be described as modifications of conic bundles.
Bernd Kreußler, Jan Stevens
wiley   +1 more source

Birational geometry of quaternions

, 2022
The Hilbert class field of the quaternion algebra $B$ is an algebra $\mathscr{H}(B)$ such that every two-sided ideal of $B$ is principal in $\mathscr{H}(B)$. We study the avatars of $B$ and $\mathscr{H}(B)$, i.e.
Nikolaev, Igor
core  

F‐purity of binomial edge ideals

Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.
Abstract In 2012, Matsuda introduced the class of weakly closed graphs and investigated when binomial edge ideals are F‐pure. He proved that weakly closed binomial edge ideals are F‐pure whenever the base field has positive characteristic. He conjectured that: (i) when the base field has characteristic 2, every F‐pure binomial edge ideal comes from a ...
Adam LaClair, Jason McCullough
wiley   +1 more source

Categorical dimension of birational automorphisms and filtrations of Cremona groups

, 2018
V3: shorter introduction, an expression in the Proof of Thm 3.5 correctedUsing a filtration on the Grothendieck ring of triangulated categories, we define the categorical dimension of a birational map between smooth projective varieties.
Bernardara, Marcello
core   +1 more source

Symplectic birational transformations of the plane [PDF]

, 2013
We study the group of symplectic birational transformations of the plane. It is proved that this group is generated by SL(2; Z), the torus and a special map of order 5, as it was conjectured by A. Usnich.
Blanc, Jérémy
core   +1 more source

Lie symmetries of birational maps preserving genus 0 fibrations [PDF]

, 2015
Preprint.We prove that any planar birational integrable map, which preserves a fibration given by genus $0$ curves has a Lie symmetry and some associated invariant measures.
Llorens, Mireia, Mañosa Fernández, Víctor   +1 more
core   +2 more sources

Motivic invariants of birational maps

Annals of Mathematics
We construct invariants of birational maps with values in the Kontsevich--Tschinkel group and in the truncated Grothendieck groups of varieties. These invariants are morphisms of groupoids and are well-suited to investigating the structure of the Grothendieck ring and L-equivalence.
Lin, Hsueh-Yung, Shinder, Evgeny
openaire   +2 more sources

On symplectic birational self-maps of projective hyperk\"{a}hler manifolds of K3$^{[n]}$-type

, 2023
We prove that projective hyperk\"{a}hler manifolds of K3$^{[n]}$-type admitting a non-trivial symplectic birational self-map of finite order are isomorphic to moduli spaces of stable (twisted) coherent sheaves on K3 surfaces. Motivated by this result, we
Prieto-Montañez, Y., Mattei, D., Mattei, Dominique, Dutta, Yajnaseni, Prieto-Montañez, Yulieth, Dutta, Y.   +5 more
core   +1 more source

Combinatorics of affine birational maps

, 2013
13 pages, 1 figure; v5: minor ...
openaire   +2 more sources

A Gröbner basis criterion for birational equivalence of affine varieties

, 1998
This paper presents a Gröbner basis criterion to determine whether a given rational map of two affine varieties is birational and if so, to compute the inverse.
Tang, Li-Zhong, Li-Zhong Tang
core   +1 more source