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

scholarly journals On minimal log discrepancies and kollár components

2021 ◽  
pp. 1-20
Author(s):  
Joaquín Moraga
Keyword(s):  
Blow Up ◽  
Chain Condition ◽  
Fano Varieties ◽  
Finite Sets ◽  
Fixed Dimension ◽  
Log Canonical ◽  
Finite Set ◽  
Canonical Singularities ◽  
Ascending Chain Condition

Abstract In this article, we prove a local implication of boundedness of Fano varieties. More precisely, we prove that $d$ -dimensional $a$ -log canonical singularities with standard coefficients, which admit an $\epsilon$ -plt blow-up, have minimal log discrepancies belonging to a finite set which only depends on $d,\,a$ and $\epsilon$ . This result gives a natural geometric stratification of the possible mld's in a fixed dimension by finite sets. As an application, we prove the ascending chain condition for minimal log discrepancies of exceptional singularities. We also introduce an invariant for klt singularities related to the total discrepancy of Kollár components.

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 Nonrational Weighted Hypersurfaces

2009 ◽  
Vol 194 ◽  
pp. 1-32 ◽  
Author(s):  
Takuzo Okada
Keyword(s):  
Arbitrary Dimension ◽  
Fano Varieties ◽  
Fano Threefolds ◽  
Alternate Proof ◽  
Quotient Singularities

AbstractThe aim of this paper is to construct (i) infinitely many families of nonrational ℚ-Fano varieties of arbitrary dimension ≥ 4 with at most quotient singularities, and (ii) twelve families of nonrational ℚ-Fano threefolds with at most terminal singularities among which two are new and the remaining ten give an alternate proof of nonrationality to known examples. These are constructed as weighted hypersurfaces with the reduction mod p method introduced by Kollár [10].

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
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