A Sharp Castelnuovo Bound for the Normalization of Certain Projective Surfaces

Nadia Chiarli

Chapter 7 in Algebraic Geometry and its Applications, 1994, pp 145-151 from Springer

Abstract: Abstract Let P be the projective r-space (r ≥ 3) over an algebraically closed field k. Consider a reduced, irreducible, complete, non-degenerate surface X ⊆ P of degree d, and let $$\bar X$$ be its normalization: we shall assume $$\bar X$$ to be smooth (which is the case, e. g., when X is the generic projection of a given smooth projective surface $$\bar X$$ ). Let ∑(n) be the linear system of curves cut out on $$\bar X$$ by the hypersurfaces of P of degree n; in other words ∑(n) corresponds to the image of the canonical map $$\rho _n :H^0 (\text{P},O_\text{P} (n)) \to H^0 (\bar X,O_{\bar X} (nD))$$ (where D is the pull-back, via the normalization morphism $$\nu :\bar X \to X$$ , of the generic hyperplane section X′ of X).

Date: 1994
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2628-4_7

Ordering information: This item can be ordered from
http://www.springer.com/9781461226284

DOI: 10.1007/978-1-4612-2628-4_7

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().