What is missing in canonical models for proper normal algebraic surfaces?

What is missing in canonical models for proper normal algebraic surfaces?

Smooth surfaces have finitely generated canonical rings and projective canonical models. For normal surfaces, however, the graded ring of multicanonical sections is possibly nonnoetherian, such that the corresponding homogeneous spectrum is noncompact. I construct a canonical compactification by add...

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Bibliographic Details
Published in:Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Vol. 71; no. 1; pp. 257 - 268
Main Author: Schröer, S.
Format: Journal Article
Language:English
Published: Heidelberg Springer Nature B.V 01-01-2001
Subjects:
Rings (mathematics)
Online Access:Get full text
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Summary:Smooth surfaces have finitely generated canonical rings and projective canonical models. For normal surfaces, however, the graded ring of multicanonical sections is possibly nonnoetherian, such that the corresponding homogeneous spectrum is noncompact. I construct a canonical compactification by adding finitely many non-ℚ-Gorenstein points at infinity, provided that each Weil divisor is numerically equivalent to a ℚ-Cartier divisor. Similar results hold for arbitrary Weil divisors instead of the canonical class.
ISSN:0025-5858
1865-8784
DOI:10.1007/BF02941475