arXiv · 2610.10439
We prove the abundance conjecture for threefolds in characteristic $>42$.
Explore connections, maps & timelines
Fabio Bernasconi, Jakub Witaszek, Zheng Xu. 2026-10-07. Abundance for threefolds in positive characteristic. https://arxiv.org/abs/2610.10439
Cite the original work for its findings. Save a collection to share your selection of sources.
KEEP EXPLORING
We show that the moduli space of curves of genus 16 is NOT of general type.
The aim of this paper is to determine minimal models of the semi-isogenous mixed surfaces with $χ=1$ and $K^2>0$ constructed by Cancian and Frapporti (Math. Nachr., 291(2-3): 264-283, 2018). In order to do this, we further develop the idea of orbit divisors introduced by Frapporti and Lee (Pac. J. Math., 318(2): 233-247, 2022), to construct effective divisors on surfaces isogenous to a product of mixed type, extending it to the semi-isogenous mixed surfaces.
If two conical symplectic resolutions $X\to X_0$ and $X^!\to X_0^!$ are symplectic dual, the cohomology ring $H^*(X)$ and the coordinate ring of $\mathbb{C}^*$-fixed points in $X_0^!$ are expected to be isomorphic as graded algebras. This statement is called Hikita conjecture and it is known that the conjecture holds for some cases. In this paper, we deal with the cohomology of framed moduli spaces over the projective plane and the coordinate ring of $\mathbb{C}^*$- fixed points of $\mathbb{C}^{2n}/((\mathbb{Z}/r\mathbb{Z})\wr S_n) $ and show that these are isomorphic as graded vector spaces. Building on subsequent work of Krylov and Shlykov on the Hikita--Nakajima conjecture for the Gieseker variety, the appendix establishes an isomorphism of graded algebras by a different approach and gives an explicit presentation by generators and relations. This revised version also corrects an error in the proof in the previous version.