Abstract
From this point on by surface we mean a nonsingular projective surface X defined over an algebraically closed field k of arbitrary characteristic. When we have to deal with surfaces with singularities, we state that explicitly (for example: let X be a normal surface...).
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Bibliographic References
Noether’s formula may be found in [BS].
The Betti numbers of an abstract algebraic surface were originally defined by Igusa (cf. [Igu]); it was later observed that they can also be introduced using étale cohomology, cf. [Del].
Details about the theory of the Picard scheme can be found in [Gro3], [Mural, Mum2], [Ser3], [Oor].
The construction and elementary properties of the Albanese variety can be found in [Ser4].
The Igusa—Severi inequality is proved in [Igu] and [Grob].
The canonical ring of a surface was first considered by Mumford [Mum3].
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© 2001 Springer Science+Business Media New York
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Bădescu, L. (2001). Noether’s Formula, the Picard Scheme, the Albanese Variety, and Plurigenera. In: Algebraic Surfaces. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3512-3_5
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DOI: https://doi.org/10.1007/978-1-4757-3512-3_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3149-8
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