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On a conjecture of Oguiso about rational curves on Calabi-Yau threefolds
Calabi-Yau threefold, rational curve, nef cone, rational points of cubic forms, Kobayashi's conjecture
2011/9/13
Abstract: Let X be a Calabi-Yau threefold. We show that if there exists on X a non-zero nef non-ample divisor then X contains a rational curve, provided its second Betti number is greater than 4.
Heterotic Non-Kahler Geometries via Polystable Bundles on Calabi-Yau Threefolds
Heterotic Non-Kahler Geometries Polystable Bundles Calabi-Yau Threefolds
2010/12/24
In arXiv:1008.1018 it is shown that a given stable vector bundle $V$ on a Calabi-Yau threefold $X$ which satisfies $c_2(X)=c_2(V)$ can be deformed to a solution of the Strominger system and the equat...
In 1977, S.-T. Yau [21] proved the famous Calabi conjecture; as a consequence we know that every compact K¨ahler manifold with vanishing first Chern class admits a Ricci-flat K¨ahler metric. This spec...
Calabi-Yau Threefolds and Moduli of Abelian Surfaces I
Calabi-Yau Threefolds Moduli of Abelian Surfaces I
2010/10/29
We describe birational models and decide the rationality/unirationality of moduli spaces AA_{d} (and AA^{lev}_{d}) of (1,d)-polarized abelian surfaces (with canonical level structure, respectively) f...