scholarly journals The spaces of rational curves on del Pezzo threefolds of degree one

2022 ◽  
Author(s):  
Nobuki Shimizu ◽  
Sho Tanimoto
Keyword(s):  
Rational Curves ◽  
Del Pezzo

scholarly journals Real singular Del Pezzo surfaces and 3-folds fibred by rational curves, II

2009 ◽  
Vol 42 (4) ◽  
pp. 531-557
Author(s):  
Fabrizio Catanese ◽  
Frédéric Mangolte
Keyword(s):  
Rational Curves ◽  
Del Pezzo Surfaces ◽  
Del Pezzo

scholarly journals Real singular Del Pezzo surfaces and threefolds fibred by rational curves, I

2008 ◽  
Vol 56 (2) ◽  
pp. 357-373 ◽  
Author(s):  
Fabrizio Catanese ◽  
Frédéric Mangolte
Keyword(s):  
Rational Curves ◽  
Del Pezzo Surfaces ◽  
Del Pezzo

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 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

scholarly journals Affine cones over cubic surfaces are flexible in codimension one

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Alexander Perepechko
Keyword(s):  
Automorphism Group ◽  
Open Subset ◽  
Pezzo Surface ◽  
Ample Divisor ◽  
Transitive Action ◽  
Del Pezzo Surface ◽  
Codimension One ◽  
Cubic Surfaces ◽  
Special Automorphism ◽  
Del Pezzo

AbstractLet Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension one. Equivalently, such a cone has an open subset with an infinitely transitive action of the special automorphism group on it.

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.

Sign in / Sign up

Export Citation Format

Share Document