Ciliberto, Ciro Dedieu, Thomas Sernesi, Edoardo
Published in
Journal für die reine und angewandte Mathematik (Crelles Journal)

Let C be a smooth projective curve (resp. ( S , L ) {(S,L)} a polarized K 3 {K3} surface) of genus g ⩾ 11 {g\geqslant 11} , with Clifford index at least 3, considered in its canonical embedding in ℙ g - 1 {\mathbb{P}^{g-1}} (resp. in its embedding in | L | ∨ ≅ ℙ g {|L|^{\vee}\cong\mathbb{P}^{g}} ). We prove that C (resp. S) is a linear section of...

Bux, Kai-Uwe Fluch, Martin G. Marschler, Marco Witzel, Stefan Zaremsky, Matthew C. B.
Published in
Journal für die reine und angewandte Mathematik (Crelles Journal)

We prove that the braided Thompson’s groups V br ${V_{\operatorname{br}}}$ and F br ${F_{\operatorname{br}}}$ are of type F ∞ ${\rm F}_{\infty}$ , confirming a conjecture by John Meier. The proof involves showing that matching complexes of arcs on surfaces are highly connected. In an appendix, Zaremsky uses these connectivity results to exhibit fam...

Fournais, Søren Sørensen, Thomas Østergaard
Published in
Journal für die reine und angewandte Mathematik (Crelles Journal)

We prove a priori bounds for all derivatives of non-relativistic Coulombic eigenfunctions ψ, involving negative powers of the distance to the singularities of the many-body potential. We use these to derive bounds for all derivatives of the corresponding one-electron densities ρ, involving negative powers of the distance from the nuclei. The result...

Urech, Christian
Published in
Journal für die reine und angewandte Mathematik (Crelles Journal)

The Cremona group is the group of birational transformations of the complex projective plane. In this paper we classify its subgroups that consist only of elliptic elements using elementary model theory. This yields in particular a description of the structure of torsion subgroups. As an application, we prove the Tits alternative for arbitrary subg...

Adler, Jeffrey D. Mishra, Manish
Published in
Journal für die reine und angewandte Mathematik (Crelles Journal)

For a connected reductive group G defined over a non-archimedean local field F, we consider the Bernstein blocks in the category of smooth representations of G(F){G(F)}. Bernstein blocks whose cuspidal support involves a regular supercuspidal representation are called regular Bernstein blocks. Most Bernstein blocks are regular when the residual ch...

Hao, Feng Schreieder, Stefan
Published in
Journal für die reine und angewandte Mathematik (Crelles Journal)

We classify all minimal models X of dimension n, Kodaira dimension n-1{n-1} and with vanishing Chern number c1n-2c2(X)=0{c_{1}^{n-2}c_{2}(X)=0}. This solves a problem of Kollár. Completing previous work of Kollár and Grassi, we also show that there is a universal constant ϵ>0{\epsilon>0} such that any minimal threefold satisfies either c1c2=0{c_...

Shu, Jie Zhai, Shuai
Published in
Journal für die reine und angewandte Mathematik (Crelles Journal)

In the present paper, we generalize the celebrated classical lemma of Birch and Heegner on quadratic twists of elliptic curves over ℚ{{\mathbb{Q}}}. We prove the existence of explicit infinite families of quadratic twists with analytic ranks 0 and 1 for a large class of elliptic curves, and use Heegner points to explicitly construct rational points...

Wang, Yu
Published in
Journal für die reine und angewandte Mathematik (Crelles Journal)

Let A be a connection of a principal bundle P over a Riemannian manifold M, such that its curvature FA∈Lloc2(M){F_{A}\in L_{\mathrm{loc}}^{2}(M)} satisfies the stationarity equation. It is a consequence of the stationarity that θA(x,r)=ecr2r4-n∫Br(x)|FA|2𝑑Vg{\theta_{A}(x,r)=e^{cr^{2}}r^{4-n}\int_{B_{r}(x)}|F_{A}|^{2}\,dV_{g}} is monotonicall...

Liu, Si-Qi Yang, Di Zhang, Youjin Zhou, Chunhui
Published in
Journal für die reine und angewandte Mathematik (Crelles Journal)

The Hodge-FVH correspondence establishes a relationship between the special cubic Hodge integrals and an integrable hierarchy, which is called the fractional Volterra hierarchy. In this paper we prove this correspondence. As an application of this result, we prove a gap condition for certain special cubic Hodge integrals and give an algorithm for c...

Raum, Sven
Published in
Journal für die reine und angewandte Mathematik (Crelles Journal)