scholarly journals On the classification of toric fano varieties

1988 ◽  
Vol 3 (1) ◽  
pp. 49-54 ◽  
Author(s):  
Günter Ewald
Keyword(s):  
Fano Varieties ◽  
Toric Fano Varieties

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 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 Studies on toric Fano varieties

2002 ◽  
Vol 23 (23) ◽  
pp. 1-99 ◽  
Author(s):  
Hiroshi SATO
Keyword(s):  
Fano Varieties ◽  
Toric Fano Varieties

Nontoric foliations by Lagrangian tori of toric Fano varieties

2010 ◽  
Vol 87 (1-2) ◽  
pp. 43-51 ◽  
Author(s):  
S. A. Belev ◽  
N. A. Tyurin
Keyword(s):  
Fano Varieties ◽  
Lagrangian Tori ◽  
Toric Fano Varieties

scholarly journals Gorenstein toric Fano varieties

2005 ◽  
Vol 116 (2) ◽  
pp. 183-210 ◽  
Author(s):  
Benjamin Nill
Keyword(s):  
Fano Varieties ◽  
Toric Fano Varieties

scholarly journals Generalized Kähler-Ricci flow on toric Fano varieties

2021 ◽  
Author(s):  
Vestislav Apostolov ◽  
Jeff Streets ◽  
Yury Ustinovskiy
Keyword(s):  
Ricci Flow ◽  
Fano Varieties ◽  
Toric Fano Varieties

scholarly journals On toric geometry and K-stability of Fano varieties

2021 ◽  
Vol 8 (19) ◽  
pp. 548-577
Author(s):  
Anne-Sophie Kaloghiros ◽  
Andrea Petracci
Keyword(s):  
Moduli Spaces ◽  
Deformation Theory ◽  
The Other ◽  
Fano Varieties ◽  
Toric Geometry ◽  
Content Type ◽  
Closed Point ◽  
Toric Fano Varieties

We present some applications of the deformation theory of toric Fano varieties to K-(semi/poly)stability of Fano varieties. First, we present two examples of K-polystable toric Fano 3 3 -fold with obstructed deformations. In one case, the K-moduli spaces and stacks are reducible near the closed point associated to the toric Fano 3 3 -fold, while in the other they are non-reduced near the closed point associated to the toric Fano 3 3 -fold. Second, we study K-stability of the general members of two deformation families of smooth Fano 3 3 -folds by building degenerations to K-polystable toric Fano 3 3 -folds.

scholarly journals Generalized GCD for toric Fano varieties

2020 ◽  
Vol 195 (4) ◽  
pp. 415-428
Author(s):  
Nathan Grieve
Keyword(s):  
Fano Varieties ◽  
Toric Fano Varieties
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