Rational Surfaces of Kodaira Type IV

Gioia Failla; Mustapha Lahyane; Giovanni Molica Bisci

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 3, page 741-750
  • ISSN: 0392-4041

Abstract

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We study the geometry of a rational surface of Kodaira type IV by giving the nature of its integral curves of self-intersection less than zero, in particular we show that they are smooth and rational. Hence, under a reasonable assumption, we prove the finite generation of its monoid of effective divisor classes and in almost all cases its anticanonical complete linear system is of projective dimension zero and of self- intersection strictly negative. Furthermore, we show that if this condition is not fulfilled, the monoid may fail to be finitely generated.

How to cite

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Failla, Gioia, Lahyane, Mustapha, and Molica Bisci, Giovanni. "Rational Surfaces of Kodaira Type IV." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 741-750. <http://eudml.org/doc/290401>.

@article{Failla2007,
abstract = {We study the geometry of a rational surface of Kodaira type IV by giving the nature of its integral curves of self-intersection less than zero, in particular we show that they are smooth and rational. Hence, under a reasonable assumption, we prove the finite generation of its monoid of effective divisor classes and in almost all cases its anticanonical complete linear system is of projective dimension zero and of self- intersection strictly negative. Furthermore, we show that if this condition is not fulfilled, the monoid may fail to be finitely generated.},
author = {Failla, Gioia, Lahyane, Mustapha, Molica Bisci, Giovanni},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {741-750},
publisher = {Unione Matematica Italiana},
title = {Rational Surfaces of Kodaira Type IV},
url = {http://eudml.org/doc/290401},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Failla, Gioia
AU - Lahyane, Mustapha
AU - Molica Bisci, Giovanni
TI - Rational Surfaces of Kodaira Type IV
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 741
EP - 750
AB - We study the geometry of a rational surface of Kodaira type IV by giving the nature of its integral curves of self-intersection less than zero, in particular we show that they are smooth and rational. Hence, under a reasonable assumption, we prove the finite generation of its monoid of effective divisor classes and in almost all cases its anticanonical complete linear system is of projective dimension zero and of self- intersection strictly negative. Furthermore, we show that if this condition is not fulfilled, the monoid may fail to be finitely generated.
LA - eng
UR - http://eudml.org/doc/290401
ER -

References

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