リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

大学・研究所にある論文を検索できる 「Periods of tropical K3 hypersurfaces」の論文概要。リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

コピーが完了しました

URLをコピーしました

論文の公開元へ論文の公開元へ
書き出し

Periods of tropical K3 hypersurfaces

山本, 悠登 東京大学 DOI:10.15083/0002003717

2022.04.20

概要

Let ∆ be a smooth reflexive polytope in dimension 3 and f be a tropical polynomial whose Newton polytope is the polar dual of ∆. One can construct a 2-sphere B equipped with an integral affine structure with singularities by contracting the tropical K3 hypersurface defined by f. We write the complement of the singularity as ι: B0 ,→ B, and the local system of integral tangent vectors on B0 as TZ. Let further Y be an anti-canonical hypersurface of the toric variety associated with the normal fan of ∆, and Pic(Y )amb be the sublattice of Pic(Y ) coming from the ambient space. We give a primitive lattice embedding Pic(Y )amb ,→ H1 (B, ι∗TZ), and compute the radiance obstruction of B, which sits in the subspace generated by the image of Pic(Y )amb.

参考文献

[GH84] William Goldman and Morris W. Hirsch, The radiance obstruction and parallel forms on affine manifolds, Trans. Amer. Math. Soc. 286 (1984), no. 2, 629–649. MR 760977

[Gro05] Mark Gross, Toric degenerations and Batyrev-Borisov duality, Math. Ann. 333 (2005), no. 3, 645–688. MR 2198802

[GS06] Mark Gross and Bernd Siebert, Mirror symmetry via logarithmic degeneration data. I, J. Differential Geom. 72 (2006), no. 2, 169–338. MR 2213573

[GS10] , Mirror symmetry via logarithmic degeneration data, II, J. Algebraic Geom. 19 (2010), no. 4, 679–780. MR 2669728

[GW00] Mark Gross and P. M. H. Wilson, Large complex structure limits of K3 surfaces, J. Differential Geom. 55 (2000), no. 3, 475–546. MR 1863732

[HU18] Kenji Hashimoto and Kazushi Ueda, Reconstruction of general elliptic K3 surfaces from their Gromov-Hausdorff limits, arXiv:1805.01719, 2018.

[HZ02] Christian Haase and Ilia Zharkov, Integral affine structures on spheres and torus fibrations of Calabi–Yau toric hypersurfaces I, arXiv:math/0205321, 2002.

[Iri11] Hiroshi Iritani, Quantum cohomology and periods, Ann. Inst. Fourier (Grenoble) 61 (2011), no. 7, 2909–2958. MR 3112512

[Iwa10] Shinsuke Iwao, Integration over tropical plane curves and ultradiscretization, Int. Math. Res. Not. IMRN (2010), no. 1, 112–148. MR 2576286

[Kaj08] Takeshi Kajiwara, Tropical toric geometry, Toric topology, Contemp. Math., vol. 460, Amer. Math. Soc., Providence, RI, 2008, pp. 197–207. MR 2428356 (2010c:14078)

[Kal15] Nikita Kalinin, A guide to tropical modifications, arXiv:1509.03443, 2015.

[KMM08] Eric Katz, Hannah Markwig, and Thomas Markwig, The j-invariant of a plane tropical cubic, J. Algebra 320 (2008), no. 10, 3832–3848. MR 2457725

[KMM09] , The tropical j-invariant, LMS J. Comput. Math. 12 (2009), 275–294. MR 2570928

[KS06] Maxim Kontsevich and Yan Soibelman, Affine structures and non-Archimedean analytic spaces, The unity of mathematics, Progr. Math., vol. 244, Birkh¨auser Boston, Boston, MA, 2006, pp. 321–385. MR 2181810

[Mik06] Grigory Mikhalkin, Tropical geometry and its applications, International Congress of Mathematicians. Vol. II, Eur. Math. Soc., Z¨urich, 2006, pp. 827–852. MR 2275625

[MZ08] Grigory Mikhalkin and Ilia Zharkov, Tropical curves, their Jacobians and theta functions, Curves and abelian varieties, Contemp. Math., vol. 465, Amer. Math. Soc., Providence, RI, 2008, pp. 203–230.

[OO18a] Yuji Odaka and Yoshiki Oshima, Collapsing K3 surfaces and Moduli compactification, Proc. Japan Acad. Ser. A Math. Sci. 94 (2018), no. 8, 81–86. MR 3859764

[OO18b] , Collapsing K3 surfaces, Tropical geometry and Moduli compactifications of Satake, Morgan-Shalen type, arXiv:1810.07685, 2018.

[Pay09] Sam Payne, Analytification is the limit of all tropicalizations, Math. Res. Lett. 16 (2009), no. 3, 543–556. MR 2511632 (2010j:14104)

[Sch73] Wilfried Schmid, Variation of Hodge structure: the singularities of the period mapping, Invent. Math. 22 (1973), 211–319. MR 0382272

[Sha15] Kristin Shaw, Tropical surfaces, arXiv:1506.07407, 2015.

[Ued14] Kazushi Ueda, Mirror symmetry and K3 surfaces, arXiv:1407.1566, 2014.

参考文献をもっと見る

全国の大学の
卒論・修論・学位論文

一発検索!

この論文の関連論文を見る