Built on

M. Besier, D. Festi, M. Harrison, and B. Naskrecki, “Arithmetic and geometry of a K3 surface emerging from virtual corrections to Drell–Yan scattering,” arXiv:1908.01079 [math.AG]
Original
1908
Earlier work this paper cites.
J. L. Bourjaily, A. J. McLeod, C. Vergu, M. Volk, M. Von Hippel, and M. Wilhelm, “Embedding Feynman Integral (Calabi-Yau) Geometries in Weighted Projective Space,” arXiv:1910.01534 [hep-th]
Original
1910
Earlier work this paper cites.
A. Klemm, C. Nega, and R. Safari, “The l l -loop Banana Amplitude from GKZ Systems and relative Calabi-Yau Periods,” JHEP
Original
1912
Earlier work this paper cites.
Wiley Classics Library. John Wiley & Sons Inc., New York, 1978
P. Griffiths and J. Harris, Principles of Algebraic Geometry · 1978
Earlier work this paper cites.
V. V. Nikulin, “Finite automorphism groups of Kählerian surfaces of type K3.,” Tr. Mosk. Mat. O.-va
1979
Earlier work this paper cites.
F. Cachazo, “Sharpening The Leading Singularity,” arXiv:0803.1988 [hep-th]
Original
1988
Earlier work this paper cites.
N. I. Usyukina and A. I. Davydychev, “Exact Results for Three and Four Point Ladder Diagrams with an Arbitrary Number of Rungs,” Phys. Lett
1993
Earlier work this paper cites.
L. Borisov, “Towards the Mirror Symmetry for Calabi-Yau Complete intersections in Gorenstein Toric Fano Varieties,” arXiv e-prints
1993
Earlier work this paper cites.
V. V. Batyrev, “Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties,” J. Alg. Geom
1994
Earlier work this paper cites.
11, 1996
P. S. Aspinwall, “K3 surfaces and string duality,” in Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 96): Fields, Strings, and Duality · 1996
Earlier work this paper cites.

Similar

V. V. Batyrev, “Stringy Hodge numbers of varieties with Gorenstein canonical singularities,” arXiv e-prints
1997
Cited alongside, same era.
P. Belkale and P. Brosnan, “Matroids, motives, and a conjecture of Kontsevich.,” Duke Math. J
2003
Cited alongside, same era.
M. Kreuzer and H. Skarke, “PALP: A Package for analyzing lattice polytopes with applications to toric geometry,” Comput. Phys. Commun
2004
Cited alongside, same era.
L. Mason and D. Skinner, “The Complete Planar S S -Matrix of 𝒩 = 4 \mathcal{N}\!=\!4 SYM as a Wilson Loop in Twistor Space,” JHEP
Original
2005
Cited alongside, same era.
J. Drummond, J. Henn, V. Smirnov, and E. Sokatchev, “Magic Identities for Conformal Four-Point Integrals,” JHEP
2007
Cited alongside, same era.

Then

A. Hodges, “Eliminating Spurious Poles from Gauge-Theoretic Amplitudes,” JHEP
Original
2013
Later among the works it cites.
A. Hodges, “The Box Integrals in Momentum-Twistor Geometry,” JHEP
Original
2013
Later among the works it cites.
S. Bloch, M. Kerr, and P. Vanhove, “A Feynman Integral via Higher Normal Functions,” Compos. Math
Original
2015
Later among the works it cites.
Cambridge University Press, 9, 2016
D. Huybrechts, Lectures on K3 Surfaces · 2016
Later among the works it cites.
S. Bloch, M. Kerr, and P. Vanhove, “Local Mirror Symmetry and the Sunset Feynman Integral,” Adv. Theor. Math. Phys
Original
2017
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…

2020

Traintrack Calabi-Yaus from Twistor Geometry

Vergu, Cristian, Volk, Matthias

Understand

We describe the geometry of the leading singularity locus of the traintrack integral family directly in momentum twistor space.

For the two-loop case, known as the elliptic double box, the leading singularity locus is a genus one curve, which we obtain as an intersection of two quadrics in $\mathbb{P}^{3}$.
At three loops, we obtain a K3 surface which arises as a branched surface over two genus-one curves in $\mathbb{P}^{1} \times \mathbb{P}^{1}$.
We present an analysis of its properties.

Built on

M. Besier, D. Festi, M. Harrison, and B. Naskrecki, “Arithmetic and geometry of a K3 surface emerging from virtual corrections to Drell–Yan scattering,” arXiv:1908.01079 [math.AG]
Original
1908
Earlier work this paper cites.
J. L. Bourjaily, A. J. McLeod, C. Vergu, M. Volk, M. Von Hippel, and M. Wilhelm, “Embedding Feynman Integral (Calabi-Yau) Geometries in Weighted Projective Space,” arXiv:1910.01534 [hep-th]
Original
1910
Earlier work this paper cites.
A. Klemm, C. Nega, and R. Safari, “The l l -loop Banana Amplitude from GKZ Systems and relative Calabi-Yau Periods,” JHEP
Original
1912
Earlier work this paper cites.
Wiley Classics Library. John Wiley & Sons Inc., New York, 1978
P. Griffiths and J. Harris, Principles of Algebraic Geometry · 1978
Earlier work this paper cites.
V. V. Nikulin, “Finite automorphism groups of Kählerian surfaces of type K3.,” Tr. Mosk. Mat. O.-va
1979
Earlier work this paper cites.
F. Cachazo, “Sharpening The Leading Singularity,” arXiv:0803.1988 [hep-th]
Original
1988
Earlier work this paper cites.
N. I. Usyukina and A. I. Davydychev, “Exact Results for Three and Four Point Ladder Diagrams with an Arbitrary Number of Rungs,” Phys. Lett
1993
Earlier work this paper cites.
L. Borisov, “Towards the Mirror Symmetry for Calabi-Yau Complete intersections in Gorenstein Toric Fano Varieties,” arXiv e-prints
1993
Earlier work this paper cites.
V. V. Batyrev, “Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties,” J. Alg. Geom
1994
Earlier work this paper cites.
11, 1996
P. S. Aspinwall, “K3 surfaces and string duality,” in Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 96): Fields, Strings, and Duality · 1996
Earlier work this paper cites.

Similar

V. V. Batyrev, “Stringy Hodge numbers of varieties with Gorenstein canonical singularities,” arXiv e-prints
1997
Cited alongside, same era.
P. Belkale and P. Brosnan, “Matroids, motives, and a conjecture of Kontsevich.,” Duke Math. J
2003
Cited alongside, same era.
M. Kreuzer and H. Skarke, “PALP: A Package for analyzing lattice polytopes with applications to toric geometry,” Comput. Phys. Commun
2004
Cited alongside, same era.
L. Mason and D. Skinner, “The Complete Planar S S -Matrix of 𝒩 = 4 \mathcal{N}\!=\!4 SYM as a Wilson Loop in Twistor Space,” JHEP
Original
2005
Cited alongside, same era.
J. Drummond, J. Henn, V. Smirnov, and E. Sokatchev, “Magic Identities for Conformal Four-Point Integrals,” JHEP
2007
Cited alongside, same era.