Dwork pencil of quintic threefolds

introduction

• The derived category of coherent sheaves on a general quintic threefold is a central object in mirror symmetry
• 1,1,27,2875, 698005,
• On a general quintic threefold \(Y\subset \mathbb{P}^4\) there are 2875 lines

memo

• http://mathoverflow.net/questions/160561/the-classical-number-2875-of-lines-on-the-quintic-as-a-dt-invariant/160846#160846
• http://mathoverflow.net/questions/215775/asymptotic-int-m-mathrmexp-mathbfe-leftn-fract2-pi-i-right-lef

related items

• Mirror symmetry
• Dwork K3 surfaces

expositions

• Pandharipande, R., and R. P. Thomas. 2011. “13/2 Ways of Counting Curves.” arXiv:1111.1552 [hep-Th], November. http://arxiv.org/abs/1111.1552.
• Zagier, https://docs.google.com/file/d/0B8XXo8Tve1cxUV9VQ3dtZjhMYjA/edit

articles

• Fité, Francesc, Kiran S. Kedlaya, and Andrew V. Sutherland. “Sato-Tate Groups of Some Weight 3 Motives.” arXiv:1212.0256 [math], December 2, 2012. http://arxiv.org/abs/1212.0256.
• Oguiso, Keiji, and Xun Yu. “Automorphism Groups of Smooth Quintic Threefolds.” arXiv:1504.05011 [math], April 20, 2015. http://arxiv.org/abs/1504.05011.
• Segal, Ed, and Richard P. Thomas. ‘Quintic Threefolds and Fano Elevenfolds’. arXiv:1410.6829 [math], 24 October 2014. http://arxiv.org/abs/1410.6829.
• Shparlinski, Igor E. “On the Density of Integer Points on the Generalised Markoff-Hurwitz and Dwork Hypersurfaces.” arXiv:1404.5866 [math], April 23, 2014. http://arxiv.org/abs/1404.5866.
• Candelas, Philip, Xenia de la Ossa, Bert van Geemen, and Duco van Straten. 2012. “Lines on the Dwork Pencil of Quintic Threefolds.” Advances in Theoretical and Mathematical Physics 16 (6): 1779–1836.
• Musta\ct\va, Anca. 2013. “Degree 1 Curves in the Dwork Pencil and the Mirror Quintic.” Mathematische Annalen 355 (1): 97–130. doi:10.1007/s00208-011-0668-x.