51 citations · 165 across the 20 of their papers we have counts for
22 papers
Equivariant birational types and derived categories
Christian Böhning, Hans-Christian Graf von Bothmer, Yuri Tschinkel
We investigate equivariant birational geometry of rational surfaces and threefolds from the perspective of derived categories.
A rigid, not infinitesimally rigid surface with K ample
Christian Böhning, Hans-Christian Graf von Bothmer, Roberto Pignatelli
We produce an example of a rigid, but not infinitesimally rigid smooth compact complex surface with ample canonical bundle using results about arrangements of lines inspired by wor…
Prelog Chow groups of self-products of degenerations of cubic threefolds
Christian Böhning, Hans-Christian Graf von Bothmer, Michel van Garrel
It is unknown whether smooth cubic threefolds have an (integral Chow-theoretic) decomposition of the diagonal, or whether they are stably rational or not in general. As a first ste…
Prelog Chow rings and degenerations
Christian Böhning, Hans-Christian Graf von Bothmer, Michel van Garrel
For a simple normal crossing variety , we introduce the concepts of prelog Chow ring, saturated prelog Chow group, as well as their counterparts for numerical equivalence. Think…
Unramified Brauer groups of conic bundle threefolds in characteristic two
Asher Auel, Alessandro Bigazzi, Christian Böhning +1
We establish a formula for computing the unramified Brauer group of tame conic bundle threefolds in characteristic 2. The formula depends on the arrangement and residue double cove…
Stable rationality of quadric and cubic surface bundle fourfolds
Asher Auel, Christian Böhning, Alena Pirutka
We study the stable rationality problem for quadric and cubic surface bundles over surfaces from the point of view of the degeneration method for the Chow group of 0-cycles. Our ma…
Degenerations of Gushel-Mukai fourfolds, with a view towards irrationality proofs
Christian Böhning, Hans-Christian Graf von Bothmer
We study a certain class of degenerations of Gushel-Mukai fourfolds as conic bundles, which we call tame degenerations and which are natural if one wants to prove that very general…
Some properties of dynamical degrees with a view towards cubic fourfolds
Christian Böhning, Hans-Christian Graf von Bothmer, Pawel Sosna
Dynamical degrees and spectra can serve to distinguish birational automorphism groups of varieties in quantitative, as opposed to only qualitative, ways. We introduce and discuss s…
On the dynamical degrees of reflections on cubic fourfolds
Christian Böhning, Hans-Christian Graf von Bothmer, Pawel Sosna
We compute the dynamical degrees of certain compositions of reflections in points on a smooth cubic fourfold. Our interest in these computations stems from the irrationality proble…
Birationally isotrivial fiber spaces
Fedor Bogomolov, Christian Böhning, Hans-Christian Graf von Bothmer
We prove that a family of varieties is birationally isotrivial if all the fibers are birational to each other.
The transcendental lattice of the sextic Fermat surface
Asher Auel, Christian Böhning, Hans-Christian Graf v. Bothmer
We prove that the integral polarized Hodge structure on the transcendental lattice of a sextic Fermat surface is decomposable. This disproves a conjecture of Kulikov related to a H…
On the Jordan-Hölder property for geometric derived categories
Christian Böhning, Hans-Christian Graf von Bothmer, Pawel Sosna
We prove that the semiorthogonal decompositions of the derived category of the classical Godeaux surface X do not satisfy the Jordan-Hölder property. More precisely, there are two…
Determinantal Barlow surfaces and phantom categories
Christian Böhning, Hans-Christian Graf von Bothmer, Ludmil Katzarkov +1
We prove that the bounded derived category of the surface S constructed by Barlow admits a length 11 exceptional sequence consisting of (explicit) line bundles. Moreover, we show t…
On the derived category of the classical Godeaux surface
Christian Böhning, Hans-Christian Graf von Bothmer, Pawel Sosna
We construct an exceptional sequence of length 11 on the classical Godeaux surface X which is the Z/5-quotient of the Fermat quintic surface in P^3. This is the maximal possible le…
Isoclinism and stable cohomology of wreath products
Fedor Bogomolov, Christian Böhning
Using the notion of isoclinism introduced by P. Hall for finite p-groups, we show that many important classes of finite p-groups have stable cohomology detected by abelian subgroup…
Stable cohomology of alternating groups
Fedor Bogomolov, Christian Böhning
In this article we determine the stable cohomology groups H^i_s (A_n, Z/p) of the alternating groups A_n for all integers n and i, and all primes p.
Birational properties of some moduli spaces related to tetragonal curves of genus 7
Christian Böhning, Hans-Christian Graf von Bothmer, Gianfranco Casnati
Let M_{7,n} be the (coarse) moduli space of smooth curves of genus 7 with n marked points defined over the complex field. We denote by M^1_{7,n;4} the locus of points inside M_{7,n…
Linear bounds for levels of stable rationality
Fedor Bogomolov, Christian Böhning, Hans-Christian Graf von Bothmer
Let G be one of the groups SL_n C, Sp_2n C, SO_m C, O_m C, or G_2. For a generically free G-representation V, we say that N is a level of stable rationality for V/G if V/G x P^N is…
Rationality of quotients by linear actions of affine groups
Fedor Bogomolov, Christian Böhning, Hans-Christian Graf von Bothmer
Let G be the (special) affine group, semidirect product of SL_n and C^n. In this paper we study the representation theory of G and in particular the question of rationality for V/G…
On the rationality of the moduli space of Lüroth quartics
Christian Böhning, Hans-Christian Graf v. Bothmer
We prove that the moduli space M_L of L"uroth quartics in P^2, i.e. the space of quartics which can be circumscribed around a complete pentagon of lines modulo the action of PGL_3(…
Rationality of moduli spaces of plane curves of small degree
Christian Böhning, Hans-Christian Graf von Bothmer, Jakob Kröker
We prove that the moduli space C(d) of plane curves of degree d (for projective equivalence) is rational except possibly if d= 6, 7, 8, 11, 12, 14, 15, 16, 18, 20, 23, 24, 26, 32,…
Rationality of the moduli spaces of plane curves of sufficiently large degree
Christian Böhning, Hans-Christian Graf v. Bothmer
We prove that the moduli space of plane curves of degree d is rational for all sufficiently large d.