Severi variety (Hilbert scheme)

Short description: Algebraic variety in a Hilbert scheme

In mathematics, a Severi variety is an algebraic variety in a Hilbert scheme that parametrizes curves in projective space with given degree and geometric genus and at most node singularities. Its dimension is 3d + g − 1.

It is a theorem that Severi varieties are algebraic varieties, i.e. it is irreducible.

References

• Maksym Fedorchuk, Severi varieties and the moduli space of curves, Ph.D. thesis, 2008.
• Joe Harris and Ian Morrison. Moduli of curves, volume 187 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1998.