Construction of rational surfaces in projective fourspace
--Hirotachi Abo

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I will talk about the construction of
five different families of smooth rational surfaces of degree 12 in 
projective fourspace. This surface is new and of interest in the 
classification of smooth non-general type surfaces in projective 
fourspace. This classification problem is motivated by the theorem of 
Ellingsrud and Peskine, which says that the degrees of such surfaces are 
bounded. Moreover, the rational surfaces in projective fourspace were 
previously known up to degree 11, and these families set
a new degree record.


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These families were found in collaboration with Kristian Ranestad.