scholarly journals Finite morphisms onto Fano manifolds of Picard number 1 which have rational curves with trivial normal bundles

2003 ◽  
Vol 12 (4) ◽  
pp. 627-651 ◽  
Author(s):  
Jun-Muk Hwang ◽  
Ngaiming Mok
Keyword(s):  
Rational Curves ◽  
Picard Number ◽  
Fano Manifolds ◽  
Normal Bundles

scholarly journals Rational curves and bounds on the Picard number of Fano manifolds

2010 ◽  
Vol 147 (1) ◽  
pp. 207-217 ◽  
Author(s):  
Carla Novelli ◽  
Gianluca Occhetta
Keyword(s):  
Rational Curves ◽  
Picard Number ◽  
Fano Manifolds

scholarly journals Normal bundles of rational curves on complete intersections

2019 ◽  
Vol 21 (02) ◽  
pp. 1850011 ◽  
Author(s):  
Izzet Coskun ◽  
Eric Riedl
Keyword(s):  
Complete Intersection ◽  
Normal Bundle ◽  
Rational Curves ◽  
Complete Intersections ◽  
Type Formula ◽  
Normal Bundles ◽  
Rationally Connected

Let [Formula: see text] be a general Fano complete intersection of type [Formula: see text]. If at least one [Formula: see text] is greater than [Formula: see text], we show that [Formula: see text] contains rational curves of degree [Formula: see text] with balanced normal bundle. If all [Formula: see text] are [Formula: see text] and [Formula: see text], we show that [Formula: see text] contains rational curves of degree [Formula: see text] with balanced normal bundle. As an application, we prove a stronger version of the theorem of Tian [27], Chen and Zhu [4] that [Formula: see text] is separably rationally connected by exhibiting very free rational curves in [Formula: see text] of optimal degrees.

scholarly journals Remarks on the normal bundles of generic rational curves

2017 ◽  
Vol 63 (2) ◽  
pp. 211-220 ◽  
Author(s):  
Alberto Alzati ◽  
Riccardo Re
Keyword(s):  
Rational Curves ◽  
Normal Bundles

scholarly journals Polarized minimal families of rational curves and higher Fano manifolds

2012 ◽  
Vol 134 (1) ◽  
pp. 87-107 ◽  
Author(s):  
Carolina Araujo ◽  
Ana-Maria Castravet
Keyword(s):  
Rational Curves ◽  
Fano Manifolds
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