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    ag.algebraic geometry - Smoothness of fix point components of …

    Let $X$ be a smooth complex algebraic variety, and $\varphi: \Gamma\curvearrowright X$ an action (by automorphisms) of a finite group $\Gamma$ on $X$. Can we say that each irreducible component of the fix point set $X^{\Gamma}$ is smooth?

    Algebraicity and smoothness of fixed point stacks - arXiv.org

    In various situations of algebraic geometry, one needs to consider the fixed points of a flat group scheme acting on an algebraic stack. Currently, probably the biggest provider

    [2205.11114] Algebraicity and smoothness of fixed point stacks

    23 Mei 2022 · Abstract: We study algebraicity and smoothness of fixed point stacks for flat group schemes which have a finite composition series whose factors are either reductive or proper, flat, finitely presented, acting on algebraic stacks with affine, finitely presented diagonal. For this, we extend some theorems of [SGA3.2] on functors of homomorphisms ...

    ag.algebraic geometry - Fixed points under a finite group action …

    16 Apr 2019 · The fixed point locus is smooth. This is more difficult to prove -- an analytic argument due to Cartan appears in Algebraic geometry and topology, and an alternative approach is Luna's étale slice theorem.

    ag.algebraic geometry - connected components of the fixed point ...

    02 Agu 2021 · Let $X$ be a smooth complex variety with an action of a finite group $G$. The fixed point subvariety $X^G$ is smooth but may have many connected components. What determines these connected components geometrically?

    Logarithmic Gromov{Witten theory with expansions

    1.1. The problem. Let Xbe a smooth projective algebraic variety, and let DˆXbe a simple normal crossings divisor with components D 1;:::;D k. Relative Gromov{Witten theory concerns maps of pairs (C;p 1;:::;p n) !(X;D); where Cis a smooth genus gcurve in a homology class , meeting the component D iat p j with contact order c ij2N. For each j ...

    AG algebraic geometry WS08/09 de Jong’s resolution of …

    AG algebraic geometry WS08/09 de Jong’s resolution of singularities and applications Main reference is [dJ]. [B1] also contains all proofs, [dJ2] is an improved ... Smoothness, semistability, and toroidal geometry. J. Algebraic Geom. 6 (1997), no. 4, 789–801. [B1] Berthelot, Pierre: Alt´erations de vari´et´es alg´ebriques (d’apr`s A ...

    Algebraicity and smoothness of fixed point stacks

    23 Mei 2022 · We study algebraicity and smoothness of fixed point stacks for flat group schemes which have a finite composition series whose factors are either reductive or proper, flat, finitely presented, acting on algebraic stacks with affine, finitely presented diagonal.

    Algebraicity and smoothness of fixed point stacks - ResearchGate

    23 Mei 2022 · Download Citation | Algebraicity and smoothness of fixed point stacks | We study algebraicity and smoothness of fixed point stacks for flat group schemes which have a finite...

    Standard stable Horikawa surfaces

    (i) If 2a⩾6m, then the linear system has no base points and the general branch divisor is smooth and connected. (ii) If 6m>2a⩾5m, then B= σ ∞+ B′and B′moves in a base-point free linear system with σ ∞·B′= 2a−5m. In particular, the general branch divisor is …