scholarly journals CLASSIFICATION OF POLARIZED SYMPLECTIC AUTOMORPHISMS OF FANO VARIETIES OF CUBIC FOURFOLDS

2015 ◽  
Vol 58 (1) ◽  
pp. 17-37 ◽  
Author(s):  
LIE FU
Keyword(s):  
Fano Varieties ◽  
Symplectic Automorphisms

AbstractWe classify the polarized symplectic automorphisms of Fano varieties of smooth cubic fourfolds (equipped with the Plücker polarization) and study the fixed loci.

scholarly journals Betti numbers and pseudoeffective cones in 2-Fano varieties

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Giosuè Emanuele Muratore
Keyword(s):  
Large Class ◽  
Betti Numbers ◽  
Fano Varieties ◽  
Higher Dimensional ◽  
Special Case ◽  
Answering Questions

Abstract The 2-Fano varieties, defined by De Jong and Starr, satisfy some higher-dimensional analogous properties of Fano varieties. We consider (weak) k-Fano varieties and conjecture the polyhedrality of the cone of pseudoeffective k-cycles for those varieties, in analogy with the case k = 1. Then we calculate some Betti numbers of a large class of k-Fano varieties to prove some special case of the conjecture. In particular, the conjecture is true for all 2-Fano varieties of index at least n − 2, and we complete the classification of weak 2-Fano varieties answering Questions 39 and 41 in [2].

scholarly journals Simple normal crossing Fano varieties and log Fano manifolds

2014 ◽  
Vol 214 ◽  
pp. 95-123
Author(s):  
Kento Fujita
Keyword(s):  
Fano Varieties ◽  
Fano Manifold ◽  
Fano Manifolds ◽  
Normal Crossing ◽  
Fano Index ◽  
Simple Normal Crossing

AbstractA projective log variety (X, D) is called alog Fano manifoldifXis smooth and ifDis a reduced simple normal crossing divisor onΧwith − (KΧ+D) ample. Then-dimensional log Fano manifolds (X, D) with nonzeroDare classified in this article when the log Fano indexrof (X, D) satisfies eitherr≥n/2withρ(X) ≥ 2 orr≥n− 2. This result is a partial generalization of the classification of logarithmic Fano 3-folds by Maeda.

scholarly journals Canonical Toric Fano Threefolds

2010 ◽  
Vol 62 (6) ◽  
pp. 1293-1309 ◽  
Author(s):  
Alexander M. Kasprzyk
Keyword(s):  
Fano Varieties ◽  
Fano Threefolds ◽  
Inductive Approach ◽  
Canonical Singularities ◽  
Toric Fano Varieties

AbstractAn inductive approach to classifying all toric Fano varieties is given. As an application of this technique, we present a classification of the toric Fano threefolds with at worst canonical singularities. Up to isomorphism, there are 674,688 such varieties.

scholarly journals Simple normal crossing Fano varieties and log Fano manifolds

2014 ◽  
Vol 214 ◽  
pp. 95-123 ◽  
Author(s):  
Kento Fujita
Keyword(s):  
Fano Varieties ◽  
Fano Manifold ◽  
Fano Manifolds ◽  
Normal Crossing ◽  
Fano Index ◽  
Simple Normal Crossing

AbstractA 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. This result is a partial generalization of the classification of logarithmic Fano 3-folds by Maeda.

scholarly journals Automorphisms and periods of cubic fourfolds

2021 ◽  
Author(s):  
Radu Laza ◽  
Zhiwei Zheng
Keyword(s):  
Fixed Point ◽  
Automorphism Group ◽  
Automorphism Groups ◽  
Leech Lattice ◽  
Torelli Theorem ◽  
Symplectic Automorphisms ◽  
Cubic Fourfold

AbstractWe classify the symplectic automorphism groups for cubic fourfolds. The main inputs are the global Torelli theorem for cubic fourfolds and the classification of the fixed-point sublattices of the Leech lattice. Among the highlights of our results, we note that there are 34 possible groups of symplectic automorphisms, with 6 maximal cases. The six maximal cases correspond to 8 non-isomorphic, and isolated in moduli, cubic fourfolds; six of them previously identified by other authors. Finally, the Fermat cubic fourfold has the largest possible order (174, 960) for the automorphism group (non-necessarily symplectic) among all smooth cubic fourfolds.

Sign in / Sign up

Export Citation Format

Share Document