Moscow Mathematical Journal

Volume 26, Issue 1, January–March 2026 pp. 73–85.

On Projective Threefolds with Two-Dimensional Space of Vanishing Cycles

Authors: Timofey Fedorov (1)
Author institution:(1) National Research University Higher School of Economics, Moscow, Russia

Summary:

We obtain a complete list of smooth projective threefolds over $\mathbb{C}$ for which the dimension of the space of vanishing cycles (in $H^2(Y,\mathbb{Q})$ of the smooth hyperplane section $Y$) equals $2$. We also obtain a complete list of rank $2$ very ample vector bundles $E$ on smooth projective surfaces with $c_2(E) = 3$.

2020 Math. Subj. Class. 14D05.

Keywords: Picard–Lefschetz theory, vector bundle.

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