Primitive Calabi-Yau threefolds

1997/01/01 by Mark Gross · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Geometry and complex manifolds #Advanced Algebra and Geometry #Calabi–Yau manifold #Mathematics #Pure mathematics #Gravitational singularity #Moduli #Divisor (algebraic geometry) #Mathematical analysis #Physics

paper · pdf · doi:10.4310/jdg/1214459799

openalex publication_date 1997/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/05

Abstract

A Calabi-Yau threefold is a complex projective threefold X (possibly with some suitable class of singularities, say terminal or canonical) with LUX = O X and h l (O X) = h 2 (O X) = 0. One of the fundamental gaps in the classification of algebraic threefolds is the lack of understanding of Calabi-Yau threefolds. Here I will try to set forth a program to bring the morass of thousands of examples of Calabi-Yaus under control.

Citations

• Topological sigma model and Donaldson-type invariants in Gromov theory
• Connecting moduli spaces of Calabi-Yau threefolds
• The moduli space of 3-folds withK=0 may nevertheless be irreducible
• Rolling among Calabi-Yau vacua
• On the connectedness of the moduli space of Calabi-Yau manifolds
• Global smoothing of Calabi-Yau threefolds
• ON ALGEBRAIC FIBER SPACE STRUCTURES ON A CALABI-YAU 3-FOLD
• Algebraic Geometry

Cited by

• Calabi-Yau coverings over some singular varieties and new Calabi-Yau 3-folds with Picard number one
• Conifold [wikipedia]