scholarly journals Even and odd instanton bundles on Fano threefolds of Picard number one

2013 ◽  
Vol 144 (1-2) ◽  
pp. 199-239 ◽  
Author(s):  
Daniele Faenzi
Keyword(s):  
Picard Number ◽  
Fano Threefolds ◽  
Instanton Bundles

scholarly journals Instanton bundles on two Fano threefolds of index 1

2020 ◽  
Vol 32 (5) ◽  
pp. 1315-1336
Author(s):  
Gianfranco Casnati ◽  
Ozhan Genc
Keyword(s):  
Irreducible Component ◽  
Moduli Space ◽  
Blow Up ◽  
Explicit Construction ◽  
Fano Threefolds ◽  
Instanton Bundles

AbstractWe deal with instanton bundles on the product {\mathbb{P}^{1}\times\mathbb{P}^{2}} and the blow up of {\mathbb{P}^{3}} along a line. We give an explicit construction leading to instanton bundles. Moreover, we also show that they correspond to smooth points of a unique irreducible component of their moduli space.

scholarly journals Instanton bundles on Fano threefolds

2012 ◽  
Vol 10 (4) ◽  
pp. 1198-1231 ◽  
Author(s):  
Alexander Kuznetsov
Keyword(s):  
Fano Threefolds ◽  
Instanton Bundles

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.

scholarly journals Instanton bundles on the Segre threefold with Picard number three

2020 ◽  
Vol 293 (6) ◽  
pp. 1026-1043
Author(s):  
V. Antonelli ◽  
F. Malaspina
Keyword(s):  
Picard Number ◽  
Instanton Bundles

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.

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.

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