Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.05158

Log Sarkisov Program for strongly $\mathbb{Q}$-factorial compact Kähler threefolds

Swapnajit Das·Roktim Mascharak
View original source ↗Read source document ↗Export metadata ↓

Abstract

We establish the log Sarkisov Program for strongly $\mathbb{Q}$-factorial compact Kähler threefolds.

Explore related subjects

math.AG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Swapnajit Das, Roktim Mascharak. 2026-10-04. Log Sarkisov Program for strongly $\mathbb{Q}$-factorial compact Kähler threefolds. https://arxiv.org/abs/2610.05158

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

KEEP EXPLORING

Related papers

arXiv2026

Les squelettes accessibles d'un espace de Berkovich

We define a class of skeletons on Berkovich analytic spaces, which we call "accessible", which contains the standard skeleton of the n-dimensional torus for every n and is preserved by G-glueing, by taking the inverse image along a morphism of relative dimension zero, and by taking the direct image along a morphism whose restriction to the involved skeleton is topologically proper.

math.AG↗
arXiv2026

Critical Points of Degenerate Metrics on Algebraic Varieties: A Tale of Overparametrization

We study the critical points over an algebraic variety of an optimization problem defined by a quadratic objective that is degenerate. This scenario arises in machine learning when the dataset size is small with respect to the model, and is typically referred to as overparametrization. Our main result relates the degenerate optimization problem to a nondegenerate one via a projection. In the highly-degenerate regime, we find that a central role is played by the ramification locus of the projection. Additionally, we provide tools for counting the number of critical points over projective varieties, and discuss specific cases arising from deep learning. Our work bridges tools from algebraic geometry with ideas from machine learning, and it extends the line of literature around the Euclidean distance degree to the degenerate setting.

math.AG↗
arXiv2026

On relative Ulrich bundles and generalized Clifford algebras

We give a Clifford-theoretic description of relatively Ulrich bundles on smooth families of hypersurfaces. A split projection centre produces an explicit monic Clifford algebra whose locally free representations are exactly the relatively Ulrich bundles. For quadric fibrations, the description is intrinsic and requires no projection centre; the even Clifford algebra gives exact formulas for the minimal relative Ulrich rank in terms of Brauer classes and monodromy. We also obtain applications to stability, moduli, and relative wildness.

math.AG↗