On the Alexander invariants of trigonal curves
نویسندگان
چکیده
We show that most of the genus-zero subgroups braid group $\mathbb{B}_3$ (which are roughly monodromy groups trigonal curves on Hirzebruch surfaces) irrelevant as far Alexander invariant is concerned: there a very restricted class \enquote{primitive} such these and their intersections determine all invariants. Then, we classify primitive in special subclass. This result implies known classification dihedral covers irreducible curves.
منابع مشابه
On Reciprocality of Twisted Alexander Invariants
Given a knot and an SLnC representation of its group that is conjugate to its dual, the representation that replaces each matrix with its inverse-transpose, the associated twisted Reidemeister torsion is reciprocal. An example is given of a knot group and SL3Z representation that is not conjugate to its dual for which the twisted Reidemeister torsion is not reciprocal.
متن کاملThe Alexander Module of a Trigonal Curve. Ii
We complete the enumeration of the possible roots of the Alexander polynomial (both conventional and over finite fields) of a trigonal curve. The curves are not assumed proper or irreducible.
متن کاملAlexander Invariants and Transversality
We show that some of the main results in Laurentiu Maxim’s paper [10] can be obtained (even in a slightly more general setting) using the theory of perverse sheaves of finite rank over Q as described for instance in author’s recent book [3].
متن کاملDihedral Coverings of Trigonal Curves
We classify and study trigonal curves in Hirzebruch surfaces admitting dihedral Galois coverings. As a consequence, we obtain certain restrictions on the fundamental group of a plane curve D with a singular point of multiplicity (deg D−3).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Revista Matematica Complutense
سال: 2021
ISSN: ['1696-8220', '1139-1138', '1988-2807']
DOI: https://doi.org/10.1007/s13163-020-00381-9