scholarly journals Birationally rigid Fano threefold hypersurfaces

2017 ◽  
Vol 246 (1167) ◽  
pp. 0-0 ◽  
Author(s):  
Ivan Cheltsov ◽  
Jihun Park
Keyword(s):  
Fano Threefold

scholarly journals Simple Helices on Fano Threefolds

2011 ◽  
Vol 54 (3) ◽  
pp. 520-526
Author(s):  
A. Polishchuk
Keyword(s):  
Braid Group ◽  
Vector Bundles ◽  
Coherent Sheaf ◽  
Derived Category ◽  
Fano Threefolds ◽  
Fano Threefold

AbstractBuilding on the work of Nogin, we prove that the braid groupB4acts transitively on full exceptional collections of vector bundles on Fano threefolds withb2= 1 andb3= 0. Equivalently, this group acts transitively on the set of simple helices (considered up to a shift in the derived category) on such a Fano threefold. We also prove that on threefolds withb2= 1 and very ample anticanonical class, every exceptional coherent sheaf is locally free.

scholarly journals Mukai-Umemura’s example of the Fano threefold with genus 12 as a compactification of C3

1992 ◽  
Vol 127 ◽  
pp. 145-165 ◽  
Author(s):  
Mikio Furushima
Keyword(s):  
Canonical Divisor ◽  
Fano Threefold

Let (X, Y) be a smooth projective compactification with the non-normal irreducible boundary Y, namely, X is a smooth projective algebraic threefold and Y a non-normal irreducible divisor on X such that X – Y is isomorphic to C3. Then Y is ample and the canonical divisor Kx on X can be written as Kx = - r Y (1 ≦ r ≦ 4).

scholarly journals The family of lines on the Fano threefold V5

1989 ◽  
Vol 116 ◽  
pp. 111-122 ◽  
Author(s):  
Mikio Furushima ◽  
Noboru Nakayama
Keyword(s):  
Linear System ◽  
Betti Number ◽  
Invertible Sheaf ◽  
The Family ◽  
Anticanonical Divisor ◽  
Fano Threefold ◽  
Ample Invertible Sheaf

A smooth projective algebraic 3-fold V over the field C is called a Fano 3-fold if the anticanonical divisor — Kv is ample. The integer g = g(V) = ½(- Kv)3 is called the genus of the Fano 3-fold V. The maximal integer r ≧ 1 such that ϑ(— Kv)≃ ℋ r for some (ample) invertible sheaf ℋ ε Pic V is called the index of the Fano 3-fold V. Let V be a Fano 3-fold of the index r = 2 and the genus g = 21 which has the second Betti number b2(V) = 1. Then V can be embedded in P6 with degree 5, by the linear system |ℋ|, where ϑ(— Kv)≃ ℋ2 (see Iskovskih [5]). We denote this Fano 3-fold V by V5.

scholarly journals Halphen pencils on weighted Fano threefold hypersurfaces

2009 ◽  
Vol 7 (1) ◽  
pp. 1-45 ◽  
Author(s):  
Ivan Cheltsov ◽  
Jihun Park
Keyword(s):  
Kodaira Dimension ◽  
Dimension Zero ◽  
Fano Threefold

AbstractOn a general quasismooth well-formed weighted hypersurface of degree Σi=14 a i in ℙ(1, a 1, a 2, a 3, a 4), we classify all pencils whose general members are surfaces of Kodaira dimension zero.

scholarly journals Bundles over the Fano Threefold V 5

2005 ◽  
Vol 33 (9) ◽  
pp. 3061-3080 ◽  
Author(s):  
Daniele Faenzi
Keyword(s):  
Fano Threefold

A weak Fano threefold arising as a blowup of a curve of genus 5 and degree 8 on $${\mathbb {P}}^3$$ P 3

2019 ◽  
Vol 5 (3) ◽  
pp. 763-770 ◽  
Author(s):  
Joseph W. Cutrone ◽  
Michael A. Limarzi ◽  
Nicholas A. Marshburn
Keyword(s):  
Fano Threefold ◽  
Weak Fano

scholarly journals On Geometry of Fano Threefold Hypersurfaces

2021 ◽  
pp. 1-14
Author(s):  
Hamid Abban ◽  
Ivan Cheltsov ◽  
Jihun Park
Keyword(s):  
Fano Threefold

scholarly journals ON THE QUANTUM COHOMOLOGY OF SOME FANO THREEFOLDS AND A CONJECTURE OF DUBROVIN

2005 ◽  
Vol 16 (08) ◽  
pp. 823-839 ◽  
Author(s):  
GIANNI CIOLLI
Keyword(s):  
Cohomology Ring ◽  
Quantum Cohomology ◽  
Exceptional Set ◽  
Fano Threefolds ◽  
Cohomology Rings ◽  
Small Quantum ◽  
Fano Threefold

In the present paper the small quantum cohomology ring of some Fano threefolds which are obtained as one- or two-curve blow-ups from ℙ3or the quadric Q3is explicitely computed. Because of systematic usage of the associativity property of quantum product only a very small and enumerative subset of Gromov–Witten invariants is needed. Then, for these threefolds the Dubrovin conjecture on the semisimplicity of quantum cohomology is proven by checking the computed quantum cohomology rings and by showing that a smooth Fano threefold X with b3(X) = 0 admits a complete exceptional set of the appropriate length.

scholarly journals Polarized endomorphisms of uniruled varieties. With an appendix by Y. Fujimoto and N. Nakayama

2009 ◽  
Vol 146 (1) ◽  
pp. 145-168 ◽  
Author(s):  
De-Qi Zhang
Keyword(s):  
Del Pezzo Surfaces ◽  
Fano Threefolds ◽  
Rationally Connected ◽  
Fano Threefold ◽  
Del Pezzo ◽  
Log Del Pezzo Surfaces

AbstractWe show that polarized endomorphisms of rationally connected threefolds with at worst terminal singularities are equivariantly built up from those on ℚ-Fano threefolds, Gorenstein log del Pezzo surfaces and ℙ1. Similar results are obtained for polarized endomorphisms of uniruled threefolds and fourfolds. As a consequence, we show that every smooth Fano threefold with a polarized endomorphism of degree greater than one is rational.

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