Calabi-Yau threefolds across quadratic singularities
S\'ebastien Picard
TL;DR
This paper reviews the geometry of Calabi-Yau threefolds, focusing on conifold transitions and recent advances in their geometrization, providing foundational and recent insights relevant to string theory.
Contribution
It offers a comprehensive overview of Calabi-Yau threefolds, especially their conifold transitions and recent developments in their geometric understanding.
Findings
Topological features of conifold transitions explained
Recent progress in geometrization of conifold transitions surveyed
Foundational aspects of Calabi-Yau geometry reviewed
Abstract
These are lecture notes on non-K\"ahler complex threefolds presented at the MATRIX program ``The geometry of moduli spaces in string theory''. We review some basics of Calabi-Yau geometry in Section 1, describe topological features of the conifold transition in Section 2, and survey recent developments on the geometrization of conifold transitions in Section 3.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds