Recent developments in toric geometry

DA Cox - arXiv preprint alg-geom/9606016, 1996 - arxiv.org
This paper will appear in the Proceedings of the 1995 Santa Cruz Summer Institute. The
paper is a survey of recent developments in the theory of toric varieties, including new …

Reflexive polyhedra, weights and toric Calabi-Yau fibrations

M Kreuzer, H Skarke - Reviews in Mathematical Physics, 2002 - World Scientific
During the last years we have generated a large number of data related to Calabi-Yau
hypersurfaces in toric varieties which can be described by reflexive polyhedra. We classified …

On Calabi-Yau complete intersections in toric varieties

VV Batyrev, LA Borisov - Higher-dimensional complex varieties …, 1996 - degruyter.com
We investigate Hodge-theoretic properties of Calabi-Yau complete intersections V of r semi-
ample divisors in^-dimensional toric Fano varieties having at most Gorenstein singularities …

Summing the instantons: Quantum cohomology and mirror symmetry in toric varieties

DR Morrison, MR Plesser - Nuclear Physics B, 1995 - Elsevier
We use the gauged linear sigma model introduced by Witten to calculate instanton
expansions for correlation functions in topological sigma models with target space a toric …

The space of stability conditions on abelian threefolds, and on some Calabi-Yau threefolds

A Bayer, E Macrì, P Stellari - Inventiones mathematicae, 2016 - Springer
We describe a connected component of the space of stability conditions on abelian
threefolds, and on Calabi-Yau threefolds obtained as (the crepant resolution of) a finite …

Stringy Hodge numbers of varieties with Gorenstein canonical singularities

VV Batyrev - arXiv preprint alg-geom/9711008, 1997 - arxiv.org
We introduce the notion of stringy E-function for an arbitrary normal irreducible algebraic
variety X with at worst log-terminal singularities. We prove some basic properties of stringy E …

Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry

VV Batyrev, DI Dais - Topology, 1996 - Elsevier
We propose a new higher dimensional version of the McKay correspondence which enables
us to understand the “Hodge numbers” assigned to singular Gorenstein varieties by …

PALP: a package for analysing lattice polytopes with applications to toric geometry

M Kreuzer, H Skarke - Computer Physics Communications, 2004 - Elsevier
We describe our package PALP of C programs for calculations with lattice polytopes and
applications to toric geometry, which is freely available on the internet. It contains routines …

Mirror manifolds in higher dimension

BR Greene, DR Morrison, MR Plesser - Communications in mathematical …, 1995 - Springer
We describe mirror manifolds in dimensions different from the familiar case of complex
threefolds. We isolate certain simplifying features present only in dimension three, and …

Global F-theory GUTs

R Blumenhagen, TW Grimm, B Jurke, T Weigand - Nuclear physics B, 2010 - Elsevier
We construct global F-theory GUT models on del Pezzo surfaces in compact Calabi–Yau
fourfolds realized as complete intersections of two hypersurface constraints. The …