ON THE PICARD NUMBER OF ALMOST FANO THREEFOLDS WITH PSEUDO-INDEX > 1

2008 ◽  
Vol 19 (02) ◽  
pp. 173-191 ◽  
Author(s):  
CINZIA CASAGRANDE ◽  
PRISKA JAHNKE ◽  
IVO RADLOFF
Keyword(s):  
Picard Number ◽  
Fano Threefolds ◽  
Canonical Singularities ◽  
Almost Fano

We study Gorenstein almost Fano threefolds X with canonical singularities and pseudoindex > 1. We show that the maximal Picard number of X is 10 in general, 3 if X is Fano, and 8 if X is toric. Moreover, we characterize the boundary cases. In the Fano case, we prove that the generalized Mukai conjecture holds.

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 On the existence of certain weak Fano threefolds of Picard number two

2017 ◽  
Vol 120 (1) ◽  
pp. 68 ◽  
Author(s):  
Maxim Arap ◽  
Joseph Cutrone ◽  
Nicholas Marshburn
Keyword(s):  
Picard Number ◽  
Fano Threefolds ◽  
Canonical Map ◽  
Blowing Up ◽  
Numerical Invariants ◽  
Weak Fano

This article settles the question of existence of smooth weak Fano threefolds of Picard number two with small anti-canonical map and previously classified numerical invariants obtained by blowing up certain curves on smooth Fano threefolds of Picard number $1$ with the exception of $12$ numerical cases.

Towards the classification of weak Fano threefolds with ρ = 2

2013 ◽  
Vol 11 (9) ◽  
Author(s):  
Joseph Cutrone ◽  
Nicholas Marshburn
Keyword(s):  
Finite Number ◽  
Type Ii ◽  
Numerical Classification ◽  
Picard Number ◽  
Fano Threefolds ◽  
Smooth Complex ◽  
Complex Projective ◽  
Extremal Ray ◽  
Weak Fano

AbstractIn this paper, examples of type II Sarkisov links between smooth complex projective Fano threefolds with Picard number one are provided. To show examples of these links, we study smooth weak Fano threefolds X with Picard number two and with a divisorial extremal ray. We assume that the pluri-anticanonical morphism of X contracts only a finite number of curves. The numerical classification of these particular smooth weak Fano threefolds is completed and the geometric existence of some numerical cases is proven.

scholarly journals Rank two aCM bundles on the del Pezzo threefold with Picard number 3

2015 ◽  
Vol 429 ◽  
pp. 413-446 ◽  
Author(s):  
Gianfranco Casnati ◽  
Daniele Faenzi ◽  
Francesco Malaspina
Keyword(s):  
Picard Number ◽  
Del Pezzo ◽  
Acm Bundles
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