Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 0704.3096

On a class of non-simply connected Calabi-Yau threefolds

Vincent Bouchard·Ron Donagi
View original source ↗Read source document ↗Export metadata ↓

Abstract

We obtain a detailed classification for a class of non-simply connected Calabi-Yau threefolds which are of potential interest for a wide range of problems in string phenomenology. These threefolds arise as quotients of Schoen's Calabi-Yau threefolds, which are fiber products over P1 of two rational elliptic surfaces. The quotient is by a freely acting finite abelian group preserving the fibrations. Our work involves a classification of restricted finite automorphism groups of rational elliptic surfaces.

Explore related subjects

math.AGhep-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Vincent Bouchard, Ron Donagi. 2008-04-14. On a class of non-simply connected Calabi-Yau threefolds. https://arxiv.org/abs/0704.3096

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

On the minimal model of semi-isogenous mixed surfaces

The aim of this paper is to determine minimal models of the semi-isogenous mixed surfaces with $χ=1$ and $K^2>0$ constructed by Cancian and Frapporti (Math. Nachr., 291(2-3): 264-283, 2018). In order to do this, we further develop the idea of orbit divisors introduced by Frapporti and Lee (Pac. J. Math., 318(2): 233-247, 2022), to construct effective divisors on surfaces isogenous to a product of mixed type, extending it to the semi-isogenous mixed surfaces.

math.AG↗
arXiv2026

The cohomology of framed moduli spaces and the coordinate ring of torus fixed points of quotient singularities

If two conical symplectic resolutions $X\to X_0$ and $X^!\to X_0^!$ are symplectic dual, the cohomology ring $H^*(X)$ and the coordinate ring of $\mathbb{C}^*$-fixed points in $X_0^!$ are expected to be isomorphic as graded algebras. This statement is called Hikita conjecture and it is known that the conjecture holds for some cases. In this paper, we deal with the cohomology of framed moduli spaces over the projective plane and the coordinate ring of $\mathbb{C}^*$- fixed points of $\mathbb{C}^{2n}/((\mathbb{Z}/r\mathbb{Z})\wr S_n) $ and show that these are isomorphic as graded vector spaces. Building on subsequent work of Krylov and Shlykov on the Hikita--Nakajima conjecture for the Gieseker variety, the appendix establishes an isomorphism of graded algebras by a different approach and gives an explicit presentation by generators and relations. This revised version also corrects an error in the proof in the previous version.

math.AG↗