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Nam-Hoon Lee

Publications and source records attributed to Nam-Hoon Lee.

13 recordsLinked to original sources
arXiv2026

Updates on Calabi-Yau manifolds from pairs of non-compact Calabi-Yau manifolds

We discuss developments in the construction of Calabi--Yau manifolds by smoothing normal crossing unions of quasi-Fano manifolds, following the introduction of this method to the physics community in 2010. We describe constructions of Calabi--Yau threefolds with unbounded second Betti numbers and with very small Hodge numbers, as well as the first non-Kähler examples in dimensions greater than three. The role of Landau--Ginzburg models in mirror constructions is also explained.

hep-th↗
arXiv2021

Calabi-Yau threefolds with non-Gorenstein involutions

The concept of non-Gorenstein involutions on Calabi-Yau threefolds is a higher dimensional generalization of non-symplectic involutions on $K3$ surfaces. We present some elementary facts about Calabi-Yau threefolds with non-Gorenstein involutions. We give a classification of the Calabi-Yau threefolds of Picard rank one with non-Gorenstein involutions whose fixed locus is not zero-dimensional.

math.AG↗
arXiv2019

Mirror pairs of Calabi-Yau threefolds from mirror pairs of quasi-Fano threefolds

We present a new construction of mirror pairs of Calabi-Yau manifolds by smoothing normal crossing varieties, consisting of two quasi-Fano manifolds. We introduce a notion of mirror pairs of quasi-Fano manifolds with anticanonical Calabi-Yau fibrations using recent conjectures about Landau-Ginzburg models. Utilizing this notion, we give pairs of normal crossing varieties and show that the pairs of smoothed Calabi-Yau manifolds satisfy the Hodge number relations of mirror symmetry. We consider quasi-Fano threefolds that are some blow-ups of Gorenstein toric Fano threefolds and build 6518 mirror pairs of Calabi-Yau threefolds, including 79 self-mirrors.

math.AG↗
arXiv2018

$d$-semistable Calabi--Yau threefolds of Type III

We develop some methods to construct normal crossing varieties whose dual complexes are two-dimensional, which are smoothable to Calabi--Yau threefolds. We calculate topological invariants of smoothed Calabi--Yau threefolds and show that several of them are new examples.

math.AG↗
arXiv2017

Calabi-Yau double coverings of Fano-Enriques threefolds

This note is a report on the observation that the Enriques-Fano threefolds with terminal cyclic quotient singularities admit Calabi-Yau threefolds as their double coverings. We calculate the invariants of those Calabi-Yau threefolds when the Picard number is one. It turns out that all of them are new examples.

math.AG↗
arXiv2011

A type of the Lefschetz hyperplane section theorem on \Q-Fano 3-folds with Picard number one and $1/2(1,1,1)$-singularities

We prove a type of the Lefschetz hyperplane section theorem on Q-Fano 3-folds with Picard number one and $1/2(1,1,1)$-singularities by using some degeneration method. As a byproduct, we obtain a new example of a Calabi-Yau 3-fold $X$ with Picard number one whose invariants are $$(H_X^3, c_2 (X) \cdot H_X, {e} (X)) = (8, 44, -88),$$ where $H_X$, $e(X)$ and $c_2(X)$ are an ample generator of $\Pic(X)$, the topological Euler characteristic number and the second Chern class of $X$ respectively.

math.AG↗
arXiv2011

K3 surfaces with non-symplectic involution and compact irreducible G_2-manifolds

We consider the connected-sum method of constructing compact Riemannian 7-manifolds with holonomy G_2 developed in math.DG/0012189. The method requires pairs of projective complex threefolds endowed with anticanonical K3 divisors, the latter `matching' via a certain non-holomorphic map. Suitable examples of threefolds were previously obtained in math.DG/0012189 by blowing up curves in Fano threefolds. In this paper, we give further suitable algebraic threefolds using theory of K3 surfaces with non-symplectic involution due to Nikulin. These threefolds are not obtainable from Fano threefolds, as above, and admit matching pairs leading to topologically new examples of compact irreducible G_2-manifolds. `Geography' of the values of Betti numbers b^2,b^3 for the new (and previously known) examples of compact irreducible G_2 manifolds is also discussed.

math.DG↗
arXiv2010

Calabi-Yau manifolds from pairs of non-compact Calabi-Yau manifolds

Most of Calabi-Yau manifolds that have been considered by physicists are complete intersection Calabi-Yau manifolds of toric varieties or some quotients of product types. Purpose of this paper is to introduce a different and rather new kind of construction method of Calabi-Yau manifolds by pasting two non-compact Calabi-Yau manifolds. We will also in some details explain a curious and mysterious similarity with construction of some $G_2$-manifolds (also called Joyce manifolds), which are base spaces for M-theory.

hep-th↗
arXiv2007

Calabi-Yau construction by smoothing normal crossing varieties

We investigate a method of construction of Calabi--Yau manifolds, that is, by smoothing normal crossing varieties. We develop some theories for calculating the Picard groups of the Calabi--Yau manifolds obtained in this method. Some applications are included, such as construction of new examples of Calabi--Yau 3-folds with Picard number one with some interesting properties.

math.AG↗