Transpolar pairs involving VEX multitopes yield smooth toric spaces whose Chern classes satisfy Todd-Hirzebruch identities and belong to deformation families of generalized complete intersections.
Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves
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abstract
We prove the Doran-Harder-Thompson conjecture in the case of elliptic curves by using ideas from SYZ mirror symmetry. The conjecture claims that when a Calabi-Yau manifold $X$ degenerates to a union of two quasi-Fano manifolds (Tyurin degeneration), a mirror Calabi-Yau manifold of $X$ can be constructed by gluing the two mirror Landau-Ginzburg models of the quasi-Fano manifolds. The two crucial ideas in our proof are to obtain a complex structure by gluing the underlying affine manifolds and to construct the theta functions from the Landau-Ginzburg superpotentials.
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Numerical Ricci-flat Calabi–Yau metrics turn string compactifications from topological existence statements into computable geometries, unlocking normalized couplings, spectra, and metric-level tests of mirror symmetry.
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Chern Characteristics and Todd-Hirzebruch Identities for Transpolar Pairs of Toric Spaces
Transpolar pairs involving VEX multitopes yield smooth toric spaces whose Chern classes satisfy Todd-Hirzebruch identities and belong to deformation families of generalized complete intersections.
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What to do with a Ricci-flat Calabi--Yau metric?
Numerical Ricci-flat Calabi–Yau metrics turn string compactifications from topological existence statements into computable geometries, unlocking normalized couplings, spectra, and metric-level tests of mirror symmetry.