Archiv der Mathematik

, Volume 81, Issue 4, pp 397–401 | Cite as

High dimensional reducible hyperplane sections with multigenera $\leq$ 1

Original paper


Let X be an algebraic submanifold of the complex projective space $\mathbb{P}^N$ of dimension $n \geq 5$. We describe those $X \subset \mathbb{P}^N$ whose intersection with some hyperplane is a smooth simply normal crossing divisor $A_{1} + \cdots + A_{r}$ with $r \geq 2$ such that $g(A_{k}, L_{A_k}) \leq 1$ for $k=1,\ldots, r$.

Mathematics Subject Classification (2000):

Primary 14C20, 14N30 Secondary 14M99 


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Copyright information

© Birkhäuser-Verlag 2003

Authors and Affiliations

  1. 1.Dipartimento di Matematica “F. Enriques”Università Statale di MilanoMilanoItaly

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