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Representations on canonical models of generalized Fermat curves and their syzygies
- Publication Year :
- 2023
-
Abstract
- We study canonical models of $\left(\mathbb{Z}/k\mathbb{Z}\right)^n$- covers of the projective line, tamely ramified at exactly $n+1$ points each of index $k$, when $k,n\geq 2$ and the characteristic of the ground field $K$ is either zero or does not divide $k$. We determine explicitly the structure of the respective homogeneous coordinate ring first as a graded $K$-algebra, next as a $\left(\mathbb{Z}/k\mathbb{Z}\right)^n$- representation over $K$, and then as a graded module over the polynomial ring; in the latter case, we give generators for its first syzygy module, which we also decompose as a direct sum of irreducible representations.
- Subjects :
- Mathematics - Algebraic Geometry
14H45, 14H30, 14F10, 13D02
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2304.02990
- Document Type :
- Working Paper