Algebr. Geom. Topol. 15 (1), 319-369, (2015) DOI: 10.2140/agt.2015.15.319
Jesse Kass, Kirsten Wickelgren
KEYWORDS: Abel map, compactified Picard scheme, compactified Jacobian, Poincaré duality, 14F35, 14D20, 14F20
For a smooth algebraic curve over a field, applying to the Abel map to the Picard scheme of modulo its boundary realizes the Poincaré duality isomorphism
We show the analogous statement for the Abel map to the compactified Picard, or Jacobian, scheme, namely this map realizes the Poincaré duality isomorphism . In particular, of this Abel map is an isomorphism.
In proving this result, we prove some results about that are of independent interest. The singular curve has a unique singularity that is an ordinary fold point, and we describe the compactified Picard scheme of such a curve up to universal homeomorphism using a presentation scheme. We construct a Mayer–Vietoris sequence for certain pushouts of schemes, and an isomorphism of functors