Birational boundedness of rationally connected Calabi-Yau 3-folds

被引：14

作者：

Chen, Weichung ^{[1
]}

Cerbo, Gabriele Di ^{[2
]}

Han, Jingjun ^{[3
]}

Jiang, Chen ^{[4
]}

Svaldi, Roberto ^{[5
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, Tokyo 1538914, Japan

[2] Princeton Univ, Dept Math, Princeton, NJ 08540 USA

[3] Johns Hopkins Univ, Dept Math, Baltimore, MD 21218 USA

[4] Fudan Univ, Shanghai Ctr Math Sci, Jiangwan Campus,2005 Songhu Rd, Shanghai 200438, Peoples R China

[5] Ecole Polytech Fed Lausanne, SB MATH GE, MA B1 497 Batiment MA,Stn 8, CH-1015 Lausanne, Switzerland

来源：

ADVANCES IN MATHEMATICS | 2021年 / 378卷

关键词：

Calabi-Yau; 3-folds; Boundedness; Rationally connected; MINIMAL LOG DISCREPANCIES; VARIETIES; UNIRATIONALITY; EXISTENCE; MODELS; PAIRS;

D O I：

10.1016/j.aim.2020.107541

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that rationally connected Calabi-Yau 3-folds with Kawamata log terminal (klt) singularities form a birationally bounded family, or more generally, rationally connected 3 folds of epsilon-CY type form a birationally bounded family for epsilon > 0. Moreover, we show that the set of epsilon-lc log Calabi-Yau pairs (X, B) with coefficients of B bounded away from zero is log bounded modulo flops. As a consequence, we deduce that rationally connected klt Calabi-Yau 3-folds with mld bounded away from 1 are bounded modulo flops. (c) 2020 Elsevier Inc. All rights reserved.

引用

页数：32

共 49 条

[1] BPS states of curves in Calabi-Yau 3-folds
Bryan, Jim
Pandharipande, Rahul
GEOMETRY & TOPOLOGY, 2001, 5 : 287 - 318
[2] Polarized Calabi-Yau 3-folds in codimension 4
Brown, Gavin
Georgiadis, Konstantinos
MATHEMATISCHE NACHRICHTEN, 2017, 290 (5-6) : 710 - 725
[3] Asymptotically cylindrical Calabi-Yau 3-folds from weak Fano 3-folds
Corti, Alessio
Haskins, Mark
Nordstroem, Johannes
Pacini, Tommaso
GEOMETRY & TOPOLOGY, 2013, 17 (04) : 1955 - 2059
[4] Construction and deformations of Calabi-Yau 3-folds in codimension 4
Mohsin, Sumayya
Nazir, Shaheen
Qureshi, Muhammad Imran
JOURNAL OF ALGEBRA, 2024, 657 : 773 - 803
[5] Gromov-Witten Theory of Calabi-Yau 3-folds
Liu, Chiu-Chu Melissa
PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS, VOL II: INVITED LECTURES, 2010, : 497 - 512
[6] Attractor mechanisms of moduli spaces of Calabi-Yau 3-folds
Fan, Yu-Wei
Kanazawa, Atsushi
JOURNAL OF GEOMETRY AND PHYSICS, 2023, 185
[7] On a class of non-simply connected Calabi-Yau 3-folds with positive Euler characteristic
Karayayla, Tolga
COMMUNICATIONS IN NUMBER THEORY AND PHYSICS, 2022, 16 (01) : 159 - 213
[8] ON THE CONNECTEDNESS OF THE STANDARD WEB OF CALABI-YAU 3-FOLDS AND SMALL TRANSITIONS
Wang, Sz-Sheng
ASIAN JOURNAL OF MATHEMATICS, 2018, 22 (06) : 981 - 1003
[9] NEW EXAMPLES OF CALABI-YAU 3-FOLDS AND GENUS ZERO SURFACES
Bini, Gilberto
Favale, Filippo F.
Neves, Jorge
Pignatelli, Roberto
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2014, 16 (02)
[10] Examples of Calabi-Yau 3-Folds of P7 with ρ=1
Bertin, Marie-Amelie
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2009, 61 (05): : 1050 - 1072

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