mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, a Castelnuovo surface is a

surface A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is t ...

of general type such that the

canonical bundle In mathematics, the canonical bundle of a non-singular algebraic variety V of dimension n over a field is the line bundle \,\!\Omega^n = \omega, which is the ''n''th exterior power of the cotangent bundle Ω on ''V''. Over the complex numbers, it ...

is very ample and such that ''c''₁² = 3''p_g'' − 7.

Guido Castelnuovo Guido Castelnuovo (14 August 1865 – 27 April 1952) was an Italian mathematician. He is best known for his contributions to the field of algebraic geometry, though his contributions to the study of statistics and probability theory are also signi ...

proved that if the canonical bundle is very ample for a surface of general type then ''c''₁² ≥ 3''p_g'' − 7.

Construction

Invariants

References

*{{Citation , last1=Barth , first1=Wolf P. , last2=Hulek , first2=Klaus , last3=Peters , first3=Chris A.M. , last4=Van de Ven , first4=Antonius , title=Compact Complex Surfaces , publisher= Springer-Verlag, Berlin , series=Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. , isbn=978-3-540-00832-3 , mr=2030225 , year=2004 , volume=4 Algebraic surfaces Complex surfaces