scholarly journals On the anti-canonical geometry of weak ℚ-Fano threefolds II

2021 ◽  
Vol 70 (6) ◽  
pp. 2473-2542
Author(s):  
Meng Chen ◽  
Chen Jiang
Keyword(s):  
Fano Threefolds

scholarly journals Instanton bundles on two Fano threefolds of index 1

2020 ◽  
Vol 32 (5) ◽  
pp. 1315-1336
Author(s):  
Gianfranco Casnati ◽  
Ozhan Genc
Keyword(s):  
Irreducible Component ◽  
Moduli Space ◽  
Blow Up ◽  
Explicit Construction ◽  
Fano Threefolds ◽  
Instanton Bundles

AbstractWe deal with instanton bundles on the product {\mathbb{P}^{1}\times\mathbb{P}^{2}} and the blow up of {\mathbb{P}^{3}} along a line. We give an explicit construction leading to instanton bundles. Moreover, we also show that they correspond to smooth points of a unique irreducible component of their moduli space.

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 Tangent scrolls in prime Fano threefolds

2000 ◽  
Vol 23 (3) ◽  
pp. 411-431 ◽  
Author(s):  
Atanas Iliev ◽  
Carmen Schuhmann
Keyword(s):  
Fano Threefolds

scholarly journals Singular Fano threefolds of genus 12

2016 ◽  
Vol 207 (7) ◽  
pp. 983-1009 ◽  
Author(s):  
Yu G Prokhorov
Keyword(s):  
Fano Threefolds

scholarly journals K3 surfaces with non-symplectic involution and compact irreducible G2-manifolds

2011 ◽  
Vol 151 (2) ◽  
pp. 193-218 ◽  
Author(s):  
ALEXEI KOVALEV ◽  
NAM-HOON LEE
Keyword(s):  
Betti Numbers ◽  
Matching Condition ◽  
K3 Surfaces ◽  
Connected Sum ◽  
Fano Threefolds ◽  
New Class ◽  
Blowing Up ◽  
G2 Manifolds

AbstractWe consider the connected-sum method of constructing compact Riemannian 7-manifolds with holonomy G2 developed by the first named author. The method requires pairs of projective complex threefolds endowed with anticanonical K3 divisors and the latter K3 surfaces should satisfy a certain ‘matching condition’ intertwining on their periods and Kähler classes. Suitable examples of threefolds were previously obtained by blowing up curves in Fano threefolds.In this paper, we give a large new class of suitable algebraic threefolds using theory of K3 surfaces with non-symplectic involution due to Nikulin. These threefolds are not obtainable from Fano threefolds as above, and admit matching pairs leading to topologically new examples of compact irreducible G2-manifolds. ‘Geography’ of the values of Betti numbers b2, b3 for the new (and previously known) examples of irreducible G2 manifolds is also discussed.

The Kähler cone in families of quasi-Fano threefolds

1998 ◽  
Vol 227 (1) ◽  
pp. 45-68 ◽  
Author(s):  
Roberto Paoletti
Keyword(s):  
Fano Threefolds
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