Group Actions on Curves and arithmetic surfaces.
Equivariant Hilbert functions, Hilbert Series and Euler characteristics.
Lifting Curves with Automorphisms.
Syzygies of Canonical Curves.
Galois Module Structure of regular differentials.
(Generalized) Fermat curves.
Group scheme actions on affine schemes.
Kostas Karagiannis: Representations on canonical models of generalized Fermat curves and their syzygies. To appear in The Quarterly Journal of Mathematics. https://arxiv.org/abs/2304.02990.
Hara Charalambous, Kostas Karagiannis and Aristides Kontogeorgis: The relative canonical Ideal of the Artin-Schreier-Kummer-Witt family of curves. Ann. Inst. Fourier (Grenoble), 73(3):1085–1113, 2023.
Hara Charalambous, Kostas Karagiannis, Sotiris Karanikolopoulos and Aristides Kontogeorgis: Computational aspects of equivariant Hilbert series of canonical rings. Computer algebra in scientific computing, 83–102, Lecture Notes in Comput. Sci., 13366, Springer, Cham, [2022], ©2022
Hara Charalambous, Kostas Karagiannis, Sotiris Karanikolopoulos and Aristides Kontogeorgis: The equivariant Hilbert Series of the Canonical Ring of Fermat Curves. Indag. Math. (N.S.) 33 (2022), no. 5, 1071–1101.
Hara Charalambous, Kostas Karagiannis, Sotiris Karanikolopoulos and Aristides Kontogeorgis: Weierstrass semigroups for maximal curves realizable as Harbater–Katz–Gabber covers. Adv. Geom. 22 (2022), no. 3, 445–450.
Huy Dang, Soumyadip Das, Kostas Karagiannis, Andrew Obus and Vaidehee Thatte: Local Oort groups and the isolated differential data criterion. J. Théor. Nombres Bordeaux 34 (2022), no. 1, 251–269.
Hara Charalambous, Kostas Karagiannis, Sotiris Karanikolopoulos and Aristides Kontogeorgis: Syzygies of Ideals of Polynomial Rings over Principal Ideal Domains. ISSAC 2020: Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation, July 2020 Pages 78–82.
Kostas Karagiannis and Peter Symonds: Transfer and norm for finite group schemes over a field.
Kostas Karagiannis and Peter Symonds: Group scheme actions on affine schemes and the Čech complex.
PhD Thesis: The Canonical Ideal and Syzygies of Curves with Automorphisms, A.U.Th. Supervised by Prof. Hara Charalambous and Prof. Aristides Kontogeorgis..
MSc Thesis: The Hilbert Scheme, University of Warwick. Supervised by Prof. Diane Maclagan.
Soumyadip Das.
Sotiris Karanikolopoulos.