Rational curves of minimal degree and characterizations of projective spaces

2006 ◽  
Vol 335 (4) ◽  
pp. 937-951 ◽  
Author(s):  
Carolina Araujo
Keyword(s):  
Projective Spaces ◽  
Rational Curves ◽  
Minimal Degree

scholarly journals Enumeration of one-nodal rational curves in projective spaces

Topology ◽  
2004 ◽  
Vol 43 (4) ◽  
pp. 793-829 ◽  
Author(s):  
A ZINGER
Keyword(s):  
Projective Spaces ◽  
Rational Curves

A Characterization of Products of Projective Spaces

2006 ◽  
Vol 49 (2) ◽  
pp. 270-280 ◽  
Author(s):  
Gianluca Occhetta
Keyword(s):  
Projective Spaces ◽  
Rational Curves

AbstractWe give a characterization of products of projective spaces using unsplit covering families of rational curves.

On the irreducibility of Hilbert scheme of surfaces of minimal degree

2013 ◽  
Vol 11 (2) ◽  
Author(s):  
Fedor Bogomolov ◽  
Viktor Kulikov
Keyword(s):  
Projective Plane ◽  
Hilbert Scheme ◽  
Special Class ◽  
Main Idea ◽  
Rational Curves ◽  
Minimal Degree ◽  
Irreducible Components

AbstractThe article contains a new proof that the Hilbert scheme of irreducible surfaces of degree m in ℙm+1 is irreducible except m = 4. In the case m = 4 the Hilbert scheme consists of two irreducible components explicitly described in the article. The main idea of our approach is to use the proof of Chisini conjecture [Kulikov Vik.S., On Chisini’s conjecture II, Izv. Math., 2008, 72(5), 901–913 (in Russian)] for coverings of projective plane branched in a special class of rational curves.

scholarly journals Counting rational curves of arbitrary shape in projective spaces

2005 ◽  
Vol 9 (2) ◽  
pp. 571-697 ◽  
Author(s):  
Aleksey Zinger
Keyword(s):  
Arbitrary Shape ◽  
Projective Spaces ◽  
Rational Curves

scholarly journals Moduli Spaces of Point Configurations and Plane Curve Counts

2019 ◽  
Author(s):  
Markus Reineke ◽  
Thorsten Weist
Keyword(s):  
Recurrence Relation ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Plane Curve ◽  
Projective Spaces ◽  
Rational Curves ◽  
Euler Characteristics ◽  
Point Configurations

Abstract We identify certain Gromov–Witten invariants counting rational curves with given incidence and tangency conditions with the Euler characteristics of moduli spaces of point configurations in projective spaces. On the Gromov–Witten side, S. Fomin and G. Mikhalkin established a recurrence relation via tropicalization, which is realized on the moduli space side using Donaldson–Thomas invariants of subspace quivers.

scholarly journals Minimal degree rational curves on real surfaces

2019 ◽  
Vol 345 ◽  
pp. 263-288
Author(s):  
Niels Lubbes
Keyword(s):  
Rational Curves ◽  
Minimal Degree

scholarly journals Rational curves in CICYs in products of two projective spaces

2016 ◽  
Vol 45 (7) ◽  
pp. 2899-2911
Author(s):  
Filippo F. Favale
Keyword(s):  
Projective Spaces ◽  
Rational Curves
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