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Abstract

Hodge–Toric Geometry Beyond CY20

Deep Bhattacharjee

Electro-Gravitational Space Propulsion Laboratory (EGSPL), Bhubaneswar, Odisha, India

Sanjeevan Singha Roy

Student, Birla Institute of Technology (BIT), Mesra, Jharkhand, India

Pallab Nandi

Junior Research Fellow, DRDO SSPL; formerly, Indian Institute of Science Education and Research (IISER), Mohanpur, West Bengal, India

271 - 918
Vol.21, Issue 1, Jan-Jun, 2026
Receiving Date: 2026-04-15
Acceptance Date: 2026-05-01
Publication Date: 2026-05-14
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http://doi.org/10.37648/ijps.v21i01.019

Abstract

This article develops a higher-dimensional research programme for Calabi–Yau geometry beyond the classical threefold setting and through the explicit CY20 horizon. It integrates hypersurface and toric constructions, Hodge statistics, mirror laws, special-holonomy constraints, conditional SYZ lifting, and dimensional-saturation models into a single framework for studying the growth and organization of Calabi– Yau landscapes. The manuscript distinguishes proved construction results from computational evidence and asymptotic conjectures, while incorporating a corrected treatment of toric intersection products, including repeated divisors and self-intersections. The resulting programme provides a systematic mathematical and computational architecture for testing higher-dimensional regularities, mirror behaviour, and possible limiting laws in Calabi–Yau geometry


Keywords: Calabi–Yau manifolds; Hodge–toric geometry; mirror symmetry; dimensional saturation; special holonomy.


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