Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.07908

Semiample perturbations over arbitrary fields

Dae-Won Lee
View original source ↗Read source document ↗Export metadata ↓

Abstract

Assuming projective log resolutions, we construct semiample perturbations over arbitrary fields that preserve all log canonical places. As an application, for divisor classes with finitely generated section rings, we characterize the existence of effective divisors yielding lc or klt pairs in terms of asymptotic orders of vanishing. We also derive minimal model and semiampleness results for generalized threefolds over $F$-finite fields of characteristic $p>5$.

Explore related subjects

math.AG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Dae-Won Lee. 2026-10-06. Semiample perturbations over arbitrary fields. https://arxiv.org/abs/2610.07908

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Bloch-Ogus theory for smooth and semi-stable schemes in mixed characteristic

We study Bloch-Ogus theory and the Gersten conjecture for homology theories with duality satisfying certain properties, in particular for étale cohomology with finite coefficients coprime to the residue characteristic of the base, for smooth and semi-stable schemes in mixed characteristic. We prove the Gersten conjecture in the smooth case and prove a special case in the semi-stable situation. As a corollary of the smooth case, we obtain the surjectivity of the Galois symbol map for arbitrary local rings over an excellent discrete valuation ring.

math.AG↗
arXiv2026

Gauge origami on broken lines

In analogy to Nekrasov's theory of gauge origami on intersecting branes, we introduce the gauge origami moduli space on broken lines. We realize this moduli space as a Quot scheme parametrising zero-dimensional quotients of a torsion sheaf on two intersecting affine lines, and describe it as a moduli space of quiver representations. We construct a virtual fundamental class and virtual structure sheaf, by which we define $K$-theoretic invariants. We compute its associated partition function for all ranks, and show that it reproduces the generating series of equivariant $χ_{y}$-genus when the moduli space is smooth. Finally, we relate our partition function with the virtual invariants of the Quot schemes of the affine plane and Nekrasov's partition function.

math.AG↗
arXiv2026

Foundations of superstack theory

In view of applications to the construction of moduli spaces of objects in algebraic supergeometry, we start a systematic study of stacks in that context. After defining a superstack as a stack over the étale site of superschemes, we define quotient superstacks, and, based on previous literature, we see that, in analogy with superschemes, every superstack has an underlying ordinary stack, which we call its bosonic reduction. Then we progressively introduce more structure, considering algebraic superspaces, Deligne-Mumford superstacks and algebraic superstacks. We study the topology of algebraic superstacks and several properties of morphisms between them. We introduce quasi-coherent sheaves, and the sheaves of relative differentials. An important issue is how to check that an algebraic superstack is Deligne-Mumford, and we generalize to this setting the usual criteria in terms of the unramifiedness of the diagonal of the stack. We study principal bundles in the category of algebraic superspaces. Two appendices are devoted to collecting the basic definitions of group superschemes and principal superbundles, and to stating and analyzing some properties of morphisms of superschemes, that are at the basis of the study of morphisms of superstacks in the main text.

math.AG↗