Mordell–Weil Lattices

Schütt, Matthias; Shioda, Tetsuji

doi:10.1007/978-981-32-9301-4_6

Cited by 31 publications

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“…Note that the same argument applied to entries 9 and 10, i.e. and no Mordell-Weil torsion is expected, again in full agreement with the tables of [18].…”

Section: Technical Appendices a 'Reading Between The Lines' Vs Mordesupporting

confidence: 77%

“…Comparing table 1 of ref. [3] with the table of Mordell-Weil torsion [18], we see that of the 28 fiber configurations corresponding to SCFT only 4 have non trivial MW torsion, namely # 24 25 16 17 fiber conf.…”

Section: Technical Appendices a 'Reading Between The Lines' Vs Mordementioning

confidence: 93%

“…Tables of allowed fibers configurations for rational elliptic surfaces may be found in refs [18,72,73]…”

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confidence: 99%

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Homological classification of 4d $$ \mathcal{N} $$ = 2 QFT. Rank-1 revisited

Caorsi

Cecotti

2019

J. High Energ. Phys.

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Argyres and co-workers started a program to classify all 4d N = 2 QFT by classifying Special Geometries with appropriate properties. They completed the program in rank-1. Rank-1 N = 2 QFT are equivalently classified by the Mordell-Weil groups of certain rational elliptic surfaces.The classification of 4d N = 2 QFT is also conjectured to be equivalent to the representation theoretic (RT) classification of all 2-Calabi-Yau categories with suitable properties. Since the RT approach smells to be much simpler than the Special-Geometric one, it is worthwhile to check this expectation by reproducing the rank-1 result from the RT side. This is the main purpose of the present paper. Along the route we clarify several issues and learn new details about the rank-1 SCFT. In particular, we relate the rank-1 classification to mirror symmetry for Fano surfaces.In the follow-up paper we apply the RT methods to higher rank 4d N = 2 SCFT.

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“…Note that the same argument applied to entries 9 and 10, i.e. and no Mordell-Weil torsion is expected, again in full agreement with the tables of [18].…”

Section: Technical Appendices a 'Reading Between The Lines' Vs Mordesupporting

confidence: 77%

Section: Technical Appendices a 'Reading Between The Lines' Vs Mordementioning

confidence: 93%

See 1 more Smart Citation

Homological classification of 4d $$ \mathcal{N} $$ = 2 QFT. Rank-1 revisited

Caorsi

Cecotti

2019

J. High Energ. Phys.

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“…Let be a connected component. The weighted sum of roots in with appropriate weights according to the ADE-type of (see, for example, [26,Theorem 5.12]) is either f φ or 2 f φ . The former case occurs when the corresponding reducible fiber is a multiple fiber, while the latter occurs when the fiber is non-multiple.…”

Section: Elliptic Fibrations Of Ymentioning

confidence: 99%

Automorphism Groups of Certain Enriques Surfaces

Brandhorst

Shimada

2021

Found Comput Math

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“…Similarly, the second configuration generally forces a 2-torsion section upon the Jacobian by [18]. But then, by [24,Cor. 8.32], there is an additive fibre in characteristic 2, ruling out this configuration as well.…”

Section: Odd Degree Curves In Characteristicmentioning

confidence: 99%

Twelve Rational curves on Enriques surfaces

Rams

Schütt

2021

Res Math Sci

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Given $$d\in {\mathbb {N}}$$ d ∈ N , we prove that any polarized Enriques surface (over any field k of characteristic $$p \ne 2$$ p ≠ 2 or with a smooth K3 cover) of degree greater than $$12d^2$$ 12 d 2 contains at most 12 rational curves of degree at most d. For $$d>2$$ d > 2 , we construct examples of Enriques surfaces of high degree that contain exactly 12 rational degree-d curves.

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Mordell–Weil Lattices

Cited by 31 publications

References 0 publications

Homological classification of 4d $$ \mathcal{N} $$ = 2 QFT. Rank-1 revisited

Homological classification of 4d $$ \mathcal{N} $$ = 2 QFT. Rank-1 revisited

Automorphism Groups of Certain Enriques Surfaces

Twelve Rational curves on Enriques surfaces

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