Let X be a surface of general type with maximal Albanese dimension: if (Formula presented.), one has (Formula presented.). We give a complete classification of surfaces for which equality holds for (Formula presented.) : these are surfaces whose canonical model is a double cover of a product elliptic surface branched over an ample divisor with at most negligible singularities which intersects the elliptic fibre twice. We also prove, in the same hypothesis, that a surface X with (Formula presented.) satisfies (Formula presented.) and we give a characterization of surfaces for which the equality holds. These are surfaces whose canonical model is a double cover of an isotrivial smooth elliptic surface branched over an ample divisor with at most negligible singularities whose intersection with the elliptic fibre is 4.
Surfaces close to the Severi lines
Conti, Federico
2022-01-01
Abstract
Let X be a surface of general type with maximal Albanese dimension: if (Formula presented.), one has (Formula presented.). We give a complete classification of surfaces for which equality holds for (Formula presented.) : these are surfaces whose canonical model is a double cover of a product elliptic surface branched over an ample divisor with at most negligible singularities which intersects the elliptic fibre twice. We also prove, in the same hypothesis, that a surface X with (Formula presented.) satisfies (Formula presented.) and we give a characterization of surfaces for which the equality holds. These are surfaces whose canonical model is a double cover of an isotrivial smooth elliptic surface branched over an ample divisor with at most negligible singularities whose intersection with the elliptic fibre is 4.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
