On projective threefolds with two-dimensional space of vanishing cycles

2025/01/22 by Fedorov, Timofey
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.13027

Abstract

We obtain a complete list of smooth projective threefolds over \mathbb C for which the dimension of the space of vanishing cycles (in H² of the smooth hyperplane section) equals 2. We also obtain a complete list of rank 2 very ample vector bundles E on smooth projective surfaces with c₂(E) = 3.

Related

• Notes on very ample vector bundles on 3-folds
• Non-vanishing theorems for rank two vector bundles on threefolds
• Vector Fields on Smooth Threefolds Vanishing on Complete Intersections
• Rank-2 ample vector bundles on some smooth rational surfaces
• Criteria for very ampleness of rank two vector bundles over ruled surfaces