Birational transformations of threefold $\mathbf{Q}$-conic bundles

Yuri Prokhorov

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arXiv · 2508.03892

Birational transformations of threefold $\mathbf{Q}$-conic bundles

Yuri Prokhorov

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Abstract

A $\mathbf{Q}$-conic bundle is a contraction $f: X\to Z$ of a three-dimensional algebraic variety $X$ to a surface~$Z$ such that the variety~$X$ has only terminal $\mathbf{Q}$-factorial singularities, the anticanonical divisor $-K_X$ is~$f$-ample, and $\uprho(X/Z)=1$. We provide an algorithm to transform a $\mathbf{Q}$-conic bundle to its standard form.

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Yuri Prokhorov. 2025-08-05. Birational transformations of threefold $\mathbf{Q}$-conic bundles. https://arxiv.org/abs/2508.03892

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