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Threefolds with Kodaira Dimension 0 or 3

Ezio Stagnaro — 2007

Bollettino dell'Unione Matematica Italiana

Using the theory of adjoints and pluricanonical adjoints, we construct three nonsingular threefolds, as desingularizations of degree six hypersurfaces in 4 , having the irregularities q 1 = q 2 = 0 and the following periodical sequences of plurigenera respectively ( p g , P 2 , P 3 , , P m , ) = ( 0 , 0 , 1 , 0 , 0 , 1 , ) , ( 0 , 0 , 0 , 1 , 0 , 0 , 0 , 1 , ) , ( 0 , 0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 1 , ) . In the Appendix, starting from the second above-mentioned example, we construct a threefold of general type with q q 1 = q 2 = 0 , p g = 1 , P 2 = 2 whose m-canonical transformation is birational if and only if m 11 .

On a Problem Posed by Luigi Campedelli

Ezio Stagnaro — 2011

Bollettino dell'Unione Matematica Italiana

We construct an irreducible degree 10 plane curve C 10 , giving the explicit equation with real coefficients, having six [3; 3] points that are not on a conic. The fairly simple equation of C 10 enables the shape of a curve, whose equation has been researched without success since 1932, to be visualized in the real plane.

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