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  • Simple groups of birational transformations in dimension two
    Comment. Math. Helv. (IF 0.854) Pub Date : 2020-06-16
    Christian Urech

    We classify simple groups that act by birational transformations on compact complex Kähler surfaces. Moreover, we show that every finitely generated simple group that acts nontrivially by birational transformations on a projective surface over an arbitrary field is finite.

    更新日期:2020-07-20
  • Poisson brackets of partitions of unity on surfaces
    Comment. Math. Helv. (IF 0.854) Pub Date : 2020-06-16
    Lev Buhovsky; Alexander Logunov; Shira Tanny

    Given an open cover of a closed symplectic manifold, consider all smooth partitions of unity consisting of functions supported in the covering sets. The Poisson bracket invariant of the cover measures how much the functions from such a partition of unity can become close to being Poisson commuting. We introduce a new approach to this invariant, which enables us to prove the lower bound conjectured

    更新日期:2020-07-20
  • Singular genuine rigidity
    Comment. Math. Helv. (IF 0.854) Pub Date : 2020-06-16
    Luis A. Florit; Felippe Guimarães

    We extend the concept of genuine rigidity of submanifolds by allowing mild singularities, mainly to obtain newglobal rigidity results and unify the known ones. As one of the consequences, we simultaneously extend and unify Sacksteder and Dajczer–Gromoll theorems by showing that any compact $n$-dimensional submanifold of $\mathbb R^{n+p}$ is singularly genuinely rigid in $\mathbb R^{n+q}$, for any $q

    更新日期:2020-07-20
  • Rational equivalence and Lagrangian tori on K3 surfaces
    Comment. Math. Helv. (IF 0.854) Pub Date : 2020-06-16
    Nick Sheridan; Ivan Smith

    Fix a symplectic K3 surface $X$ homologically mirror to an algebraic K3 surface $Y$ by an equivalence taking a graded Lagrangian torus $L \subset X$ to the skyscraper sheaf of a point $y \in Y$. We show there are Lagrangian tori with vanishing Maslov class in $X$ whose class in the Grothendieck group of the Fukaya category is not generated by Lagrangian spheres. This is mirror to a statement about

    更新日期:2020-07-20
  • Algebraic varieties are homeomorphic to varieties defined over number fields
    Comment. Math. Helv. (IF 0.854) Pub Date : 2020-06-16
    Adam Parusiński; Guillaume Rond

    We show that every affine or projective algebraic variety defined over the field of real or complex numbers is homeomorphic to a variety defined over the field of algebraic numbers. We construct such a homeomorphism by carefully choosing a small deformation of the coefficients of the original equations. This deformation preserves all polynomial relations over $\mathbb Q$ satisfied by these coefficients

    更新日期:2020-07-20
  • Connected components of strata of Abelian differentials over Teichmüller space
    Comment. Math. Helv. (IF 0.854) Pub Date : 2020-06-16
    Aaron Calderon

    This paper describes connected components of the strata of holomorphic abelian differentials on marked Riemann surfaces with prescribed degrees of zeros. Unlike the case for unmarked Riemann surfaces, we find there can be many connected components, distinguished by roots of the cotangent bundle of the surface. In the course of our investigation we also characterize the images of the fundamental groups

    更新日期:2020-07-20
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