Surfaces in ℙ⁴ lying on small degree hypersurfaces

2016/09/13 by Naie, Daniel, Reider, Igor
#14J60 #14M07 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1609.03706

Abstract

Since the work of Ellingsrud and Peskine at the end of 1980s, it has been known that, with the exception of a finite number of families, smooth compact complex surfaces in ℙ⁴ with prescribed Chern classes must lie on hypersurfaces of degree m≤ 5. The study of surfaces lying on a small degree hypersurface in ℙ⁴---small meaning ≤5---seems to be a way of obtaining empirical data leading to a better conceptual understanding of surfaces in ℙ⁴. From this perspective, two main issues are considered in the paper: - an analogue of the Hartshorne-Lichtenbaum finiteness results for smooth surfaces of general type contained in a small degree hypersurface in ℙ⁴, - a study of the irregularity of smooth surfaces contained in a small degree hypersurface in ℙ⁴.

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