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 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 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

scholarly journals Nonrational Weighted Hypersurfaces

2009 ◽  
Vol 194 ◽  
pp. 1-32 ◽  
Author(s):  
Takuzo Okada
Keyword(s):  
Arbitrary Dimension ◽  
Fano Varieties ◽  
Fano Threefolds ◽  
Alternate Proof ◽  
Quotient Singularities

AbstractThe aim of this paper is to construct (i) infinitely many families of nonrational ℚ-Fano varieties of arbitrary dimension ≥ 4 with at most quotient singularities, and (ii) twelve families of nonrational ℚ-Fano threefolds with at most terminal singularities among which two are new and the remaining ten give an alternate proof of nonrationality to known examples. These are constructed as weighted hypersurfaces with the reduction mod p method introduced by Kollár [10].

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