scholarly journals On the normal bundles of rational curves on Fano 3-folds

2012 ◽  
Vol 16 (2) ◽  
pp. 237-270 ◽  
Author(s):  
Mingmin Shen
Keyword(s):  
Rational Curves ◽  
Normal Bundles

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 Normal Bundles to Laufer Rational Curves in Local Calabi–Yau Threefolds

2006 ◽  
Vol 76 (1) ◽  
pp. 57-63
Author(s):  
U. Bruzzo ◽  
A. Ricco
Keyword(s):  
Rational Curves ◽  
Normal Bundles

Normal bundles of rational curves inP 3

1980 ◽  
Vol 33 (2) ◽  
pp. 111-128 ◽  
Author(s):  
Franco Ghione ◽  
Gianni Sacchiero
Keyword(s):  
Rational Curves ◽  
Normal Bundles

scholarly journals Normal bundles of rational curves in projective space

2017 ◽  
Vol 288 (3-4) ◽  
pp. 803-827 ◽  
Author(s):  
Izzet Coskun ◽  
Eric Riedl
Keyword(s):  
Projective Space ◽  
Rational Curves ◽  
Normal Bundles

scholarly journals Rational curves on Del Pezzo manifolds

2018 ◽  
Vol 18 (4) ◽  
pp. 451-465
Author(s):  
Adrian Zahariuc
Keyword(s):  
Simple Formula ◽  
Rational Curves ◽  
Del Pezzo Surfaces ◽  
Fano Varieties ◽  
Normal Bundles ◽  
Splitting Type ◽  
Del Pezzo

Abstract We exploit an elementary specialization technique to study rational curves on Fano varieties of index one less than their dimension, known as del Pezzo manifolds. First, we study the splitting type of the normal bundles of the rational curves. Second, we prove a simple formula relating the number of rational curves passing through a suitable number of points in the case of threefolds and the analogous invariants for del Pezzo surfaces.

scholarly journals Non Kählerian surfaces with a cycle of rational curves

2021 ◽  
Vol 8 (1) ◽  
pp. 208-222
Author(s):  
Georges Dloussky
Keyword(s):  
Deformation Theory ◽  
Complex Surface ◽  
Rational Curves ◽  
Intersection Form ◽  
Connected Component ◽  
Hirzebruch Surface ◽  
Compact Complex Surface ◽  
A Chain

Abstract Let S be a compact complex surface in class VII0 + containing a cycle of rational curves C = ∑Dj . Let D = C + A be the maximal connected divisor containing C. If there is another connected component of curves C ′ then C ′ is a cycle of rational curves, A = 0 and S is a Inoue-Hirzebruch surface. If there is only one connected component D then each connected component Ai of A is a chain of rational curves which intersects a curve Dj of the cycle and for each curve Dj of the cycle there at most one chain which meets Dj . In other words, we do not prove the existence of curves other those of the cycle C, but if some other curves exist the maximal divisor looks like the maximal divisor of a Kato surface with perhaps missing curves. The proof of this topological result is an application of Donaldson theorem on trivialization of the intersection form and of deformation theory. We apply this result to show that a twisted logarithmic 1-form has a trivial vanishing divisor.

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