Results 71 to 80 of about 10,755 (178)
Fano varieties with conjecturally largest Fano index
International Journal of MathematicsFor Fano varieties of various singularities such as canonical and terminal, we construct examples with large Fano index growing doubly exponentially with dimension. By low-dimensional evidence, we conjecture that our examples have the largest Fano index for all dimensions.
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Birationally rigid Fano varieties
, 2003 We give a brief survey of the concept of birational rigidity, from its origins in the two-dimensional birational geometry, to its current state. The main ingredients of the method of maximal singularities are discussed. The principal results of the theory of birational rigidity of higher-dimensional Fano varieties and fibrations are given and certain ...
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Equivariant Kuznetsov components for cubic fourfolds with a symplectic involution
Bulletin of the London Mathematical Society, Volume 58, Issue 2, February 2026.Abstract We study the equivariant Kuznetsov component KuG(X)$\mathrm{Ku}_G(X)$ of a general cubic fourfold X$X$ with a symplectic involution. We show that KuG(X)$\mathrm{Ku}_G(X)$ is equivalent to the derived category Db(S)$D^b(S)$ of a K3$K3$ surface S$S$, where S$S$ is given as a component of the fixed locus of the induced symplectic action on the ...
Laure Flapan, Sarah Frei, Lisa Marquand
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Toric amplitudes and universal adjoints
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract A toric amplitude is a rational function associated with a simplicial polyhedral fan. The definition is inspired by scattering amplitudes in particle physics. We prove algebraic properties of such amplitudes and study the geometry of their zero loci. These hypersurfaces play the role of Warren's adjoint via a dual volume interpretation.
Simon Telen
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Simple normal crossing Fano varieties and log Fano manifolds [PDF]
Nagoya Mathematical Journal, 2014 Abstract A projective log variety (X, D) is called a log Fano manifold if X is smooth and if D is a reduced simple normal crossing divisor on Χ with − (KΧ + D) ample. The n-dimensional log Fano manifolds (X, D) with nonzero D are classified in this article when the log Fano index r of (X, D) satisfies either r ≥ n/2 with ρ(X) ≥ 2 or r ≥ n − 2.
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Coregularity of Fano varieties
Geometriae DedicataAbstractThe absolute regularity of a Fano variety, denoted by $$\hat{\textrm{reg}}(X)$$ reg ^ ( X ) , is ...
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Sulla razionalità delle 3-varietà di Fano con B_2 almeno 2
Le Matematiche, 1992 Complex, smooth, projective Fano varieties were classified by Iskovskih when B2 =1 (B2 is the second Betti number) and by Mori and Mukai when B2 is at least 2. When B2 =1 it is known if such varieties are rational (unirational) or not; in this paper we
Alberto Alzati, Marina Bertolini
doaj
Fano Varieties and Fano Polytopes
, 2020 The foundation of this thesis is the problem whether a given (normal) Gorenstein Fano variety can be degenerated to a toric Gorenstein Fano variety. We will only consider those degenerations that are compatible with the choice of an ample line bundle on the original variety and an ample rational Cartier divisor on the toric variety.
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Generalized Futaki Invariant of Almost Fano Toric Varieties, Examples
, 1998 The interpretation, due to T. Mabuchi, of the classical Futaki invariant of Fano toric manifolds is extended to the case of the Generalized Futaki invariant, introduced by W. Ding and G. Tian, of almost Fano toric varieties. As an application it is shown
Yotov, Mirroslav Tz.
core