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Intersection theory on non-commutative surfaces
Author(s):
Peter
Jørgensen
Journal:
Trans. Amer. Math. Soc.
352
(2000),
5817-5854.
MSC (2000):
Primary 14A22, 16W50
Posted:
June 21, 2000
MathSciNet review:
1695026
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Abstract:
Consider a non-commutative algebraic surface,  , and an effective divisor  on  , as defined by Van den Bergh. We show that the Riemann-Roch theorem, the genus formula, and the self intersection formula from classical algebraic geometry generalize to this setting. We also apply our theory to some special cases, including the blow up of  in a point, and show that the self intersection of the exceptional divisor is  . This is used to give an example of a non-commutative surface with a commutative  which cannot be blown down, because its self intersection is  rather than  . We also get some results on Hilbert polynomials of modules on  .
References:
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Additional Information:
Peter
Jørgensen
Affiliation:
Matematisk Afdeling, Københavns Universitet, Universitetsparken 5, 2100 København Ø, DK-Danmark
Email:
popjoerg@math.ku.dk
DOI:
10.1090/S0002-9947-00-02565-4
PII:
S 0002-9947(00)02565-4
Keywords:
Quasi-scheme,
effective divisor,
intersection multiplicity,
non-commutative surface,
non-commutative Riemann-Roch theorem,
non-commutative blow up
Received by editor(s):
June 16, 1998
Received by editor(s) in revised form:
March 31, 1999
Posted:
June 21, 2000
Copyright of article:
Copyright
2000,
American Mathematical Society
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