European Journal of Mathematics
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Massey products in mapping tori
European Journal of Mathematics - Tập 3 - Trang 34-42 - 2016
Let $$\phi :M\rightarrow M$$ be a diffeomorphism of a $$C^{\infty }$$ compact
connected manifold, and X its mapping torus. There is a natural fibration
$$p:X\rightarrow S^1$$ , denote by the corresponding cohomology class. Let
$$\lambda \in {\mathbb {C}}^*$$ . Consider the endomorphism $$\phi _k^*$$
induced by $$\phi $$ in the cohomology of M of degree k, and denote by
$$J_k(\lambda )$$ the maxima...
A strong version of Implicit Function Theorem
European Journal of Mathematics - Tập 2 Số 2 - Trang 418-443 - 2016
Length functions exponentially distorted on subgroups of complex Lie groups
European Journal of Mathematics - Tập 9 - Trang 1-17 - 2023
We introduce a notion of a length function exponentially distorted on a
(compactly generated) subgroup of a locally compact group. We prove that for a
connected linear complex Lie group there is a maximum equivalence class of
length functions exponentially distorted on a normal integral subgroup lying
between the exponential and nilpotent radicals. Moreover, a function in this
class admits an asym...
Examples of cylindrical Fano fourfolds
European Journal of Mathematics - Tập 2 - Trang 262-282 - 2015
We construct four different families of smooth Fano fourfolds with Picard
rank 1, which contain cylinders, i.e., Zariski open subsets of the form
$$Z\,{\times }\,{\mathbb {A}}^{1}$$ , where Z is a quasiprojective variety. The
affine cones over such a fourfold admit effective $${\mathbb {G}}_{{\text
{a}}}$$ -actions. Similar constructions of cylindrical Fano threefolds were done
previously in the p...
Real frontiers of fake planes
European Journal of Mathematics - Tập 2 - Trang 140-168 - 2015
In Dubouloz and Mangolte (Fake real planes: exotic affine algebraic models of
$${\mathbb {R}}^{2}$$ , arXiv:1507.01574 , 2015), we define and partially
classify fake real planes, that is, minimal complex surfaces with conjugation
whose real locus is diffeomorphic to the euclidean real plane $$\mathbb
{R}^{2}$$ . Classification results are given up to biregular isomorphisms and up
to birational dif...
Geodesic flows of c-projectively equivalent metrics are quantum integrable
European Journal of Mathematics - Tập 8 - Trang 1566-1601 - 2022
Given two c-projectively equivalent metrics on a Kähler manifold, we show that
canoncially constructed Poisson-commuting integrals of motion of the geodesic
flow, linear and quadratic in momenta, also commute as quantum operators. The
methods employed here also provide a proof of a similar statement in the case of
projective equivalence. We also investigate the addition of potentials, i.e. the
gen...
Derived categories of toric varieties III
European Journal of Mathematics - Tập 2 - Trang 196-207 - 2015
We prove that the derived McKay correspondence holds for the cases of finite
abelian groups and subgroups of $$\mathrm{GL}(2,\mathbf {C})$$ . We also prove
that K-equivalent toric birational maps are decomposed into toric flops.
The Amit–Ashurst conjecture for finite metacyclic p-groups
European Journal of Mathematics - Tập 9 - Trang 1-13 - 2023
The Amit conjecture about word maps on finite nilpotent groups has been shown to
hold for certain classes of groups. The generalised Amit conjecture says that
the probability of an element occurring in the image of a word map on a finite
nilpotent group G is either 0, or at least 1/|G|. Noting the work of Ashurst, we
name the generalised Amit conjecture the Amit–Ashurst conjecture and show that
th...
Isogenous components of Jacobian surfaces
European Journal of Mathematics - Tập 6 - Trang 1276-1302 - 2019
Let be a genus 2 curve defined over a field K, $$\mathrm{char}\,K = p \geqslant
0$$ , and its Jacobian, where $$\iota $$ is the principal polarization of
attached to . Assume that is (n, n)-geometrically reducible with $$E_1$$ and
$$E_2$$ its elliptic components. We prove that there are only finitely many
curves (up to isomorphism) defined over K such that $$E_1$$ and $$E_2$$ are
N-isogenous for $...
An introduction to the algebraic geometry of the Putman–Wieland conjecture
European Journal of Mathematics - Tập 9 - Trang 1-25 - 2023
We give algebraic and geometric perspectives on our prior results toward the
Putman–Wieland conjecture. This leads to interesting new constructions of
families of “origami” curves whose Jacobians have high-dimensional isotrivial
isogeny factors. We also explain how a hyperelliptic analogue of the
Putman–Wieland conjecture fails, following work of Marković.
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