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Machine learning the dimension of a Fano variety [PDF]

Nature Communications, 2023
Fano varieties are basic building blocks in geometry – they are ‘atomic pieces’ of mathematical shapes. Recent progress in the classification of Fano varieties involves analysing an invariant called the quantum period.
Tom Coates, Alexander M. Kasprzyk, Sara Veneziale   +2 more
doaj   +6 more sources

Symmetries of Fano varieties [PDF]

Journal für die reine und angewandte Mathematik (Crelles Journal), 2023
Prokhorov and Shramov proved that the BAB conjecture, which Birkar later proved, implies the uniform Jordan property for automorphism groups of complex Fano varieties of fixed dimension.
L. Esser, L. Ji, Joaquín Moraga
semanticscholar   +3 more sources

Complements and coregularity of Fano varieties [PDF]

Forum of Mathematics, Sigma, 2022
We study the relation between the coregularity, the index of log Calabi–Yau pairs and the complements of Fano varieties. We show that the index of a log Calabi–Yau pair $(X,B)$ of coregularity $1$ is at most $120\lambda ^2$ , where
Fernando Figueroa, Stefano Filipazzi, Joaquín Moraga, Junyao Peng   +3 more
doaj   +2 more sources

Coregularity of Fano varieties [PDF]

Geometriae Dedicata, 2022
The absolute regularity of a Fano variety, denoted by reg^(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength ...
Joaquín Moraga
semanticscholar   +4 more sources

A remark on the motive of the Fano variety of lines of a cubic [PDF]

Annales Mathematiques Du Quebec, 2016
Let X be a smooth cubic hypersurface, and let F be the Fano variety of lines on X. We establish a relation between the Chow motives of X and F. This relation implies in particular that if X has finite-dimensional motive (in the sense of Kimura), then F ...
Robert Laterveer, Laterveer Robert
exaly   +2 more sources

Polarized Endomorphisms of Fano Varieties With Complements [PDF]

International Mathematics Research Notices
Let $X$ be a Fano type variety and $(X,\Delta )$ be a log Calabi–Yau pair with $\Delta $ a Weil divisor. If $(X,\Delta )$ admits a polarized endomorphism, then we show that $(X,\Delta )$ is a finite quotient of a toric pair.
Joaquín Moraga, Jos'e Ignacio Y'anez, Wern Yeong   +2 more
semanticscholar   +3 more sources

Generalized Optimal Degenerations of Fano Varieties

Peking Mathematical Journal
We prove a generalization of the algebraic version of Tian conjecture. Precisely, for any smooth strictly increasing function $g:\mathbb{R}\to\mathbb{R}_{>0}$ with ${\rm log}\circ g$ convex, we define the $\mathbf{H}^g$-invariant on a Fano variety $X ...
Linsheng Wang
semanticscholar   +3 more sources

Ladders on Fano varieties

Journal of Mathematical Sciences, 1999
AMSTeX, 13 pages; revised: minor typos ...
exaly   +4 more sources

The Fano variety of lines of a cuspidal cyclic cubic fourfold [PDF]

ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2022
We prove that the Fano variety of lines of a cuspidal cyclic cubic fourfold is a symplectic variety with transversal A2-singularities and we study the properties of the nonsymplectic order three automorphism induced by the covering automorphism on the ...
Samuel Boissière, Tobias Heckel, A. Sarti   +2 more
semanticscholar   +1 more source

Fano and Weak Fano Hessenberg Varieties

Michigan Mathematical Journal, 2023
Regular semisimple Hessenberg varieties are smooth subvarieties of the flag variety, and their examples contain the flag variety itself and the permutohedral variety which is a toric variety. We give a complete classification of Fano and weak Fano regular semisimple Hessenberg varieties in type A in terms of combinatorics of Hessenberg functions.
Abe, Hiraku, Fujita, Naoki, Zeng, Haozhi
openaire   +3 more sources