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 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 Nef and big divisors on toric weak Fano 3-folds

2014 ◽  
Vol 9 ◽  
pp. 661-675
Author(s):  
Shoetsu Ogata
Keyword(s):  
Weak Fano

scholarly journals Asymptotically cylindrical Calabi–Yau 3–folds from weak Fano 3–folds

2013 ◽  
Vol 17 (4) ◽  
pp. 1955-2059 ◽  
Author(s):  
Alessio Corti ◽  
Mark Haskins ◽  
Johannes Nordström ◽  
Tommaso Pacini
Keyword(s):  
Weak Fano

scholarly journals On the existence of certain weak Fano threefolds of Picard number two

2017 ◽  
Vol 120 (1) ◽  
pp. 68 ◽  
Author(s):  
Maxim Arap ◽  
Joseph Cutrone ◽  
Nicholas Marshburn
Keyword(s):  
Picard Number ◽  
Fano Threefolds ◽  
Canonical Map ◽  
Blowing Up ◽  
Numerical Invariants ◽  
Weak Fano

This article settles the question of existence of smooth weak Fano threefolds of Picard number two with small anti-canonical map and previously classified numerical invariants obtained by blowing up certain curves on smooth Fano threefolds of Picard number $1$ with the exception of $12$ numerical cases.

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