arXiv subjects

Riku Kurama

Publications and source records attributed to Riku Kurama.

3 recordsLinked to original sources

arXiv2026

Fourier-Mukai partners of abelian varieties and K3 surfaces in positive and mixed characteristics

We study Fourier-Mukai equivalences of (families of) abelian varieties and K3 surfaces in positive and mixed characteristics. We first prove in any characteristics that Fourier-Mukai partners of abelian varieties are again abelian varieties. We subsequently focus on the canonical lifts of ordinary abelian varieties and ordinary K3 surfaces. For such schemes, we show that Fourier-Mukai equivalences on the special fibers can be lifted to the canonical lifts. We also prove that the relative Fourier-Mukai partners of the canonical lifts are in bijection with the Fourier-Mukai partners of the special fibers. We conclude by demonstrating that the last result can be used to recover the ordinary case of a result originally proved by Honigs, Lombardi and Tirabassi.

math.AG↗

arXiv2025

Weyl-invariant subspaces are (usually) not generic

Let $V$ be a linear representation of a connected complex reductive group $G$. Given a choice of character $θ$ of $G$, Geometric Invariant Theory defines a locus $V^{ss}_θ(G) \subseteq V$ of semistable points. We give necessary, sufficient, and in some cases equivalent conditions for the existence of $θ$ such that a maximal torus $T$ of $G$ acts on $V^{ss}_θ(T)$ with finite stabilizers. In such cases, the stack quotient $[V^{ss}_θ(G)/G]$ is is known to be Deligne-Mumford. Our proof uses the combinatorial structure of the weights of irreducible representations of semisimple groups. As an application we generalize the Grassmannian flop example of Donovan-Segal.

math.RT↗

arXiv2024

Countability of relative Fourier-Mukai partners

Anel and Toën proved that a smooth projective complex variety has only countably many smooth projective Fourier-Mukai partners up to isomorphism. This is generalized in the Stacks Project to the case where the varieties are smooth proper over an arbitrary algebraically closed field. This note will upgrade the proof of the latter reference to show that a smooth proper scheme over a noetherian base has only countably many relative Fourier-Mukai partners up to isomorphism.

math.AG↗