scholarly journals On the existence of almost Fano threefolds with del Pezzo fibrations

2016 ◽  
Vol 290 (8-9) ◽  
pp. 1281-1302 ◽  
Author(s):  
Takeru Fukuoka
Keyword(s):  
Fano Threefolds ◽  
Del Pezzo ◽  
Almost Fano

scholarly journals On stable rationality of Fano threefolds and del Pezzo fibrations

2019 ◽  
Vol 2019 (751) ◽  
pp. 275-287 ◽  
Author(s):  
Brendan Hassett ◽  
Yuri Tschinkel
Keyword(s):  
Fano Threefolds ◽  
Stable Rationality ◽  
Del Pezzo

AbstractWe prove that very general non-rational Fano threefolds which are not birational to cubic threefolds are not stably rational.

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.

scholarly journals Chern-Simons: Fano and Calabi-Yau

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Amihay Hanany ◽  
Yang-Hui He
Keyword(s):  
Algebraic Geometry ◽  
Complete Classification ◽  
Simons Theory ◽  
Del Pezzo Surfaces ◽  
Fano Threefolds ◽  
Del Pezzo ◽  
Chern Simons ◽  
Chern Simons Theory

We present the complete classification of smooth toric Fano threefolds, known to the algebraic geometry literature, and perform some preliminary analyses in the context of brane tilings and Chern-Simons theory on M2-branes probing Calabi-Yau fourfold singularities. We emphasise that these 18 spaces should be as intensely studied as their well-known counterparts: the del Pezzo surfaces.

scholarly journals The maximal unipotent finite quotient, unusual torsion in Fano threefolds, and exceptional Enriques surfaces

2020 ◽  
Vol Volume 4 ◽  
Author(s):  
Andrea Fanelli ◽  
Stefan Schröer
Keyword(s):  
Algebraic Group ◽  
Del Pezzo Surfaces ◽  
Fano Threefolds ◽  
Group Schemes ◽  
Enriques Surfaces ◽  
Finite Quotient ◽  
Del Pezzo

We introduce and study the maximal unipotent finite quotient for algebraic group schemes in positive characteristics. Applied to Picard schemes, this quotient encodes unusual torsion. We construct integral Fano threefolds where such unusual torsion actually appears. The existence of such threefolds is surprising, because the torsion vanishes for del Pezzo surfaces. Our construction relies on the theory of exceptional Enriques surfaces, as developed by Ekedahl and Shepherd-Barron. Comment: 29 pages; minor changes

ON THE PICARD NUMBER OF ALMOST FANO THREEFOLDS WITH PSEUDO-INDEX > 1

2008 ◽  
Vol 19 (02) ◽  
pp. 173-191 ◽  
Author(s):  
CINZIA CASAGRANDE ◽  
PRISKA JAHNKE ◽  
IVO RADLOFF
Keyword(s):  
Picard Number ◽  
Fano Threefolds ◽  
Canonical Singularities ◽  
Almost Fano

We study Gorenstein almost Fano threefolds X with canonical singularities and pseudoindex > 1. We show that the maximal Picard number of X is 10 in general, 3 if X is Fano, and 8 if X is toric. Moreover, we characterize the boundary cases. In the Fano case, we prove that the generalized Mukai conjecture holds.

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 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.

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