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Correction: On the Severi problem in arbitrary characteristic |
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| Authors: | Christ Karl He Xiang Tyomkin Ilya |
| Institution: | 1.Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, Be’er Sheva, 84105, Israel ;2.Institute of Algebraic Geometry, Leibniz University Hannover, Welfengarten 1, 30167, Hanover, Germany ;3.Yau Mathematical Sciences Center, Ningzhai, Tsinghua University, Haidian District, Beijing, 100084, China ;4.Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Giv’at Ram, Jerusalem, 91904, Israel ; |
| Abstract: | In this paper, we show that Severi varieties parameterizing irreducible reduced planar curves of a given degree and geometric genus are either empty or irreducible in any characteristic. Following Severi’s original idea, this gives a new proof of the irreducibility of the moduli space of smooth projective curves of a given genus in positive characteristic. It is the first proof that involves no reduction to the characteristic zero case. As a further consequence, we generalize Zariski’s theorem to positive characteristic and show that a general reduced planar curve of a given geometric genus is nodal. |
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