scholarly journals Deformation of quintic threefolds to the chordal variety

2018 ◽  
Vol 370 (9) ◽  
pp. 6493-6513
Author(s):  
Adrian Zahariuc
Keyword(s):  
Quintic Threefolds

scholarly journals A Modular Quintic Calabi-Yau Threefold of Level 55

2011 ◽  
Vol 63 (3) ◽  
pp. 616-633 ◽  
Author(s):  
Edward Lee
Keyword(s):  
Modular Form ◽  
Parameter Space ◽  
Quintic Threefolds

Abstract In this note we search the parameter space of Horrocks–Mumford quintic threefolds and locate a Calabi–Yau threefold that is modular, in the sense that the L-function of its middle-dimensional cohomology is associated with a classical modular form of weight 4 and level 55.

Degenerations of quintic threefolds and their lines

1983 ◽  
Vol 50 (4) ◽  
pp. 1127-1135 ◽  
Author(s):  
Sheldon Katz
Keyword(s):  
Quintic Threefolds

scholarly journals Automorphism groups of smooth quintic threefolds

2019 ◽  
Vol 23 (2) ◽  
pp. 201-256 ◽  
Author(s):  
Keiji Oguiso ◽  
Xun Yu
Keyword(s):  
Automorphism Groups ◽  
Quintic Threefolds

scholarly journals Thin monodromy in Sp(4)

2014 ◽  
Vol 150 (3) ◽  
pp. 333-343 ◽  
Author(s):  
Christopher Brav ◽  
Hugh Thomas
Keyword(s):  
Monodromy Group ◽  
Artin Group ◽  
Real Rank ◽  
Quintic Threefold ◽  
Monodromy Groups ◽  
Amalgamated Products ◽  
Dihedral Type ◽  
Quintic Threefolds

AbstractWe show that some hypergeometric monodromy groups in ${\rm Sp}(4,\mathbf{Z})$ split as free or amalgamated products and hence by cohomological considerations give examples of Zariski dense, non-arithmetic monodromy groups of real rank $2$. In particular, we show that the monodromy group of the natural quotient of the Dwork family of quintic threefolds in $\mathbf{P}^{4}$ splits as $\mathbf{Z}\ast \mathbf{Z}/5\mathbf{Z}$. As a consequence, for a smooth quintic threefold $X$ we show that the group of autoequivalences $D^{b}(X)$ generated by the spherical twist along ${\mathcal{O}}_{X}$ and by tensoring with ${\mathcal{O}}_{X}(1)$ is an Artin group of dihedral type.

scholarly journals Lines on the Dwork pencil of quintic threefolds

2012 ◽  
Vol 16 (6) ◽  
pp. 1779-1836 ◽  
Author(s):  
Philip Candelas ◽  
Bert van Geemen ◽  
Xenia de la Ossa ◽  
Duco van Straten
Keyword(s):  
Dwork Pencil ◽  
Quintic Threefolds
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