Abstract
In this paper we want to extend results of Kodaira [4], Horikawa [1], and Wahl [14] concerning infinitesimal families of surfaces with generic singularities over the complex numbers to fields of arbitrary characteristic. The main obstruction in getting complete analogy will be the nonexistence of a proof of Kodaira's Vanishing Theoreme which we substitute by partial results. Characteristic 2 provides for extra difficulties but in 6. we state a result which combines this paper with an interesting statement of Roberts in [12], Besides this we look at a common obstructionspace for various deformation functors. The main technique is to compare on the surface the intrinsically defined Jacobi- and conductor ideal sheaves. In contrast to [1] and [4] we work as Wahl [14] completely in an algebraic category.
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Lindner, M. Über die Moduln algebraischer Flächen. Manuscripta Math 21, 273–292 (1977). https://doi.org/10.1007/BF01167880
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DOI: https://doi.org/10.1007/BF01167880