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Journal of the European Mathematical Society

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Volume 11, Issue 6, 2009, pp. 1385–1427
DOI: 10.4171/JEMS/185

Published online: 2009-12-23

Geometry of the theta divisor of a compactified jacobian

Lucia Caporaso

The object of this paper is the theta divisor of the compactified jacobian of a nodal curve. We determine its irreducible components and give it a geometric interpretation. A characterization of hyperelliptic irreducible stable curves is appended as an application.

Keywords: Nodal curve, line bundle, compactified Picard scheme, theta divisor, Abel map, hyperelliptic stable curve.

Caporaso Lucia: Geometry of the theta divisor of a compactified jacobian. J. Eur. Math. Soc. 11 (2009), 1385-1427. doi: 10.4171/JEMS/185