Generalization of Quartic and Quintic Calabi – Yau Manifolds Fibered by Polarized K3 Surfaces

Abstract

Abstract I will present Calabi-Yau manifolds emphasizing quartic and quintic variety considering Bogomolov-Gieseker Inequality with two specific types of Clifford inequality for associated fibers by Polarized K3 surfaces with the case considered upon threefolds. Generalizations have been made to a different form of quintics with coordinates and associated mirrors for the hypersurface being concerned with taking multi-homogeneous polynomials where necessary. Minimal Calabi-Yau threefold considered for fiber varieties I0, I+, II0, II+, III, 0.