On Fano Schemes of Toric Varieties [PDF]
SIAM Journal on Applied Algebra and Geometry, 2017 Let $X_\mathcal{A}$ be the projective toric variety corresponding to a finite set of lattice points $\mathcal{A}$. We show that irreducible components of the Fano scheme $\mathbf{F}_k(X_\mathcal{A})$ parametrizing $k$-dimensional linear subspaces of $X_\mathcal{A}$ are in bijection to so-called maximal Cayley structures for $\mathcal{A}$. We explicitly
Nathan Owen Ilten, Alexandre Zotine
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Variation of stable birational types in positive characteristic [PDF]
Épijournal de Géométrie Algébrique, 2020 Let k be an uncountable algebraically closed field and let Y be a smooth projective k-variety which does not admit a decomposition of the diagonal. We prove that Y is not stably birational to a very general hypersurface of any given degree and dimension.
Stefan Schreieder
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FANO HYPERSURFACES WITH ARBITRARILY LARGE DEGREES OF IRRATIONALITY
Forum of Mathematics, Sigma, 2020 We show that complex Fano hypersurfaces can have arbitrarily large degrees of irrationality. More precisely, if we fix a Fano index $e$, then the degree of irrationality of a very general complex Fano hypersurface of index $e$ and dimension n is bounded ...
NATHAN CHEN, DAVID STAPLETON
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Asymptotic Chow Semistability Implies Ding Polystability for Gorenstein Toric Fano Varieties
Mathematics, 2023 In this paper, we prove that if a Gorenstein toric Fano variety (X,−KX) is asymptotically Chow semistable, then it is Ding polystable with respect to toric test configurations (Theorem 3).
Naoto Yotsutani
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Narrow-band and highly absorbing fano resonance in a cavity-coupled dielectric metasurface
Materials Research Express, 2023 Metamaterial resonance offers a flexibility in engineering the frequency and bandwidth of light absorption for a variety of optoelectronic applications such as wavelength-selective photodetection, optical sensing and infrared camouflaging etc.
Jiachen Yu +5 more
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X‐ray magnetic circular dichroism
Major Reference Works, Page 508-515., 2022 International Tables for Crystallography is the definitive resource and reference work for crystallography and structural science.
Each of the eight volumes in the series contains articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the ...
Gerrit van der Laan C. Chantler +2 more
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Sharp bounds on the height of K-semistable Fano varieties I, the toric case [PDF]
Compositio Mathematica, 2022 Inspired by K. Fujita's algebro-geometric result that complex projective space has maximal degree among all K-semistable complex Fano varieties, we conjecture that the height of a K-semistable metrized arithmetic Fano variety $\mathcal {X}$ of relative ...
Rolf Andreasson, Robert J. Berman
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Invariants of Fano Varieties in Families [PDF]
Moscow Mathematical Journal, 2018 11 pages. Corrected mistake in appendix.
Gounelas, Frank, Javanpeykar, Ariyan
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Computing Galois groups of Fano problems [PDF]
Journal of symbolic computation, 2022 A Fano problem consists of enumerating linear spaces of a fixed dimension on a variety, generalizing the classical problem of 27 lines on a cubic surface.
Thomas Yahl
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Algebraic uniqueness of Kähler–Ricci flow limits and optimal degenerations of Fano varieties [PDF]
Geometry & Topology, 2020 We prove that for any $\mathbb{Q}$-Fano variety $X$, the special $\mathbb{R}$-test configuration that minimizes the $H$-functional is unique and has a K-semistable $\mathbb{Q}$-Fano central fibre $(W, \xi)$.
Jiyuan Han, Chi Li
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