Noether’s Formula, the Picard Scheme, the Albanese Variety, and Plurigenera
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...).
KeywordsAbelian Variety Betti Number Group Scheme Invertible Sheaf Quadratic Transformation
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- Noether’s formula may be found in [BS].Google Scholar
- 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].Google Scholar
- Details about the theory of the Picard scheme can be found in [Gro3], [Mural, Mum2], [Ser3], [Oor].Google Scholar
- The construction and elementary properties of the Albanese variety can be found in [Ser4].Google Scholar
- The Igusa—Severi inequality is proved in [Igu] and [Grob].Google Scholar
- The canonical ring of a surface was first considered by Mumford [Mum3].Google Scholar