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A note on a Brill-Noether locus over a non-hyperelliptic curve of genus 4

100%
Huh S.
Open Mathematics
|
2009
|
tom 7
|
nr 4
617-622
EN
We prove that a certain Brill-Noether locus over a non-hyperelliptic curve C of genus 4, is isomorphic to the Donagi-Izadi cubic threefold in the case when the pencils of the two trigonal line bundles of C coincide.
2
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Threefolds with big and nef anticanonical bundles II

76%
Jahnke P., Peternell T., Radloff I.
Open Mathematics
|
2011
|
tom 9
|
nr 3
449-488
EN
In a follow-up to our paper [Threefolds with big and nef anticanonical bundles I, Math. Ann., 2005, 333(3), 569–631], we classify smooth complex projective threefolds Xwith −K X big and nef but not ample, Picard number γ(X) = 2, and whose anticanonical map is small. We assume also that the Mori contraction of X and of its flop X + are not both birational.
3
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Towards the classification of weak Fano threefolds with ρ = 2

76%
Cutrone J., Marshburn N.
Open Mathematics
|
2013
|
tom 11
|
nr 9
1552-1576
EN
In this paper, examples of type II Sarkisov links between smooth complex projective Fano threefolds with Picard number one are provided. To show examples of these links, we study smooth weak Fano threefolds X with Picard number two and with a divisorial extremal ray. We assume that the pluri-anticanonical morphism of X contracts only a finite number of curves. The numerical classification of these particular smooth weak Fano threefolds is completed and the geometric existence of some numerical cases is proven.
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