1. The construction problem for Hodge numbers modulo an integer in positive characteristic
- Author
-
Remy van Dobben de Bruyn and Matthias Paulsen
- Subjects
Statistics and Probability ,Polynomial ,Modulo ,Serre duality ,01 natural sciences ,Theoretical Computer Science ,Combinatorics ,Mathematics - Algebraic Geometry ,14G17 Positive characteristic ground fields in algebraic geometry ,Mathematics::Algebraic Geometry ,Integer ,FOS: Mathematics ,Discrete Mathematics and Combinatorics ,14A10 Varieties and morphisms ,14F99 (Primary), 14G17, 14A10, 14E99, 14F40 (Secondary) ,ddc:510 ,0101 mathematics ,Algebraically closed field ,Algebraic Geometry (math.AG) ,Mathematical Physics ,14E99 None of the above, but in this section ,Mathematics ,Algebra and Number Theory ,010102 general mathematics ,Primary: 14F99 None of the above, but in this section ,Dewey Decimal Classification::500 | Naturwissenschaften::510 | Mathematik ,010101 applied mathematics ,Computational Mathematics ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,14F99 None of the above, but in this section [Primary] ,Geometry and Topology ,Analysis - Abstract
Let $k$ be an algebraically closed field of positive characteristic. For any integer $m \geq 2$, we show that the Hodge numbers of a smooth projective $k$-variety can take on any combination of values modulo $m$, subject only to Serre duality. In particular, there are no non-trivial polynomial relations between the Hodge numbers., Published version. 15 pages
- Published
- 2020