European Journal of Mathematics

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Massey products in mapping tori
European Journal of Mathematics - Tập 3 - Trang 34-42 - 2016
Andrei Pajitnov
Let $$\phi :M\rightarrow M$$ be a diffeomorphism of a $$C^{\infty }$$ compact connected mani...... hiện toàn bộ
A weak Fano threefold arising as a blowup of a curve of genus 5 and degree 8 on $${\mathbb {P}}^3$$
European Journal of Mathematics - Tập 5 - Trang 763-770 - 2019
Joseph W. Cutrone, Michael A. Limarzi, Nicholas A. Marshburn
This article constructs a smooth weak Fano threefold of Picard number two with small anticanonical morphism that arises as a blowup of a smooth curve of genus 5 and degree 8 in $${\mathbb {P}}^3$$ . While the existence of this weak Fano was known ...... hiện toàn bộ
Length functions exponentially distorted on subgroups of complex Lie groups
European Journal of Mathematics - Tập 9 - Trang 1-17 - 2023
Oleg Yu. Aristov
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...... hiện toàn bộ
Geodesic flows of c-projectively equivalent metrics are quantum integrable
European Journal of Mathematics - Tập 8 - Trang 1566-1601 - 2022
Jan Schumm
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...... hiện toàn bộ
Derived categories of toric varieties III
European Journal of Mathematics - Tập 2 - Trang 196-207 - 2015
Yujiro Kawamata
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.
An introduction to the algebraic geometry of the Putman–Wieland conjecture
European Journal of Mathematics - Tập 9 - Trang 1-25 - 2023
Aaron Landesman, Daniel Litt
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.
Generic polynomials for cyclic function field extensions over certain finite fields
European Journal of Mathematics - - 2018
Sophie Marques
Rigid hyperholomorphic sheaves remain rigid along twistor deformations of the underlying hyparkähler manifold
European Journal of Mathematics - Tập 5 - Trang 964-1012 - 2019
Eyal Markman, Sukhendu Mehrotra, Misha Verbitsky
Let S be a K3 surface and M a smooth and projective 2n-dimensional moduli space of stable coherent sheaves on S. Over $$M\times M$$ there exists a rank $$2n-2$$ ...... hiện toàn bộ
Normalizers of maximal tori and real forms of Lie groups
European Journal of Mathematics - - 2022
A. Gerasimov, Д. В. Лебедев, Sergey Oblezin
AbstractGiven a complex connected reductive Lie group G with a maximal torus $$H\subset G$$ H ⊂ G , Tits defined an extension $$W_G^{\mathrm{T}}$$ W G T of the corresponding Weyl group $$W_G$$ W G . The extended group is supplied with an embedding into the normalizer $$N_G(H)$$ N G ( H ) such that $$W_G^{\mathrm{T}}$$ W G T together with H generate $$N_G(H)$$ N G ( H ) . In this paper we propose an interpretation of the Tits classical construction in terms of the maximal split real form $$G(\mathbb {R})\subset G$$ G ( R ) ⊂ G , which leads to a simple topological description of $$W^{\mathrm{T}}_G$$ W G T . We also consider a variation of the Tits construction associated with compact real form U of G. In this case we define an extension $$W_G^U$$ W G U of the Weyl group $$W_G$$ W G , naturally embedded into the group extension $$\widetilde{U}:=U\,{\rtimes }\, \Gamma $$ U ~ : = U ⋊ Γ of the compact real form U by the Galois group $$\Gamma ={\mathrm{Gal}}(\mathbb {C}/\mathbb {R})$$ Γ = Gal ( C / R ) . Generators of $$W^U_G$$ W G U are squared to identity as in the Weyl group $$W_G$$ W G . However, the non-trivial action of $$\Gamma $$ Γ by outer automorphisms requires $$W^U_G$$ W G U to be a non-trivial extension of $$W_G$$ W G . This gives a specific presentation of the maximal torus normalizer of the group extension $${\widetilde{U}}$$ U ~ . Finally, we describe explicitly the adjoint action of $$W_G^{\mathrm{T}}$$ hiện toàn bộ
Osculating behavior of the Kummer surface in
European Journal of Mathematics - Tập 4 Số 1 - Trang 372-380 - 2018
Mezzetti, Emilia
In an article of 1967 Edge gave a description of some beautiful geometric properties of the Kummer surface complete intersection of three quadrics in . Working on it, Dye proved in 1982 and 1992 that all its osculating spaces have dimension less than the expected 5. Here we discuss these results, also in the light of some recent result about varieties with hypo-osculating behaviour.
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