Abel maps and presentation schemes
作者:
Eduardo Esteves,
Mathieu Gagné,
Steven Kleiman,
期刊:
Communications in Algebra
(Taylor Available online 2000)
卷期:
Volume 28,
issue 12
页码: 5961-5992
ISSN:0092-7872
年代: 2000
DOI:10.1080/00927870008827199
出版商: Gordon and Breach Science Publishers Ltd.
关键词: 14H40 (Primary);14H20 (Secondary)
数据来源: Taylor
摘要:
We sharpen the two main tools used to treat the compactified Jacobian of a singular curve: Abel maps and presentation schemes. First we prove a smoothness theorem for bigraded Abel maps. Second we study the two complementary filtrations provided by the images of certain Abel maps and certain presentation schemes. Third we study a lifting of the Abel map of bidegree (m, 1) to the corresponding presentation scheme. Fourth we prove that, if a curve is blown up at a double point, then the corresponding presentation scheme is a1-bundle. Finally, using Abel maps of bidegree (m, 1), we characterize the curves having double points at worst.
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