Elliptic Calabi-Yau threefolds over a del Pezzo surface

2013/12/03 by Simon Rose, Rose, Simon, Noriko Yui +1
Mathematics · #11F11 #14H52 #14N10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1312.0911

openalex publication_date 2013/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider certain elliptic threefolds over the projective plane (more generally over certain rational surfaces) with a section in Weierstrass normal form. In particular, over a del Pezzo surface of degree 8, these elliptic threefolds are Calabi-Yau threefolds. We will discuss especially the generating functions of Gromov-Witten and Gopakumar-Vafa invariants.

Related

• Projections of del Pezzo surfaces and Calabi--Yau threefolds
• Calabi-Yau threefolds of type K (I): Classification
• Calabi--Yau 3-folds from projective joins of del Pezzo manifolds
• A rigid Calabi--Yau 3-fold
• On the modularity of Calabi-Yau threefolds containing elliptic ruled surfaces