ترغب بنشر مسار تعليمي؟ اضغط هنا

Fundamental group of Galois covers of degree $6$ surfaces

109   0   0.0 ( 0 )
 نشر من قبل Uriel Sinichkin
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

In this paper we consider the Galois covers of algebraic surfaces of degree 6, with all associated planar degenerations. We compute the fundamental groups of those Galois covers, using their degeneration. We show that for 8 types of degenerations the fundamental group of the Galois cover is non-trivial and for 20 types it is trivial. Moreover, we compute the Chern numbers of all the surfaces with this type of degeneration and prove that the signatures of all their Galois covers are negative. We formulate a conjecture regarding the structure of the fundamental groups of the Galois covers based on our findings. With an appendix by the authors listing the detailed computations and an appendix by Guo Zhiming classifying degree 6 planar degenerations.



قيم البحث

اقرأ أيضاً

Let $X$ be an algebraic surface of degree $5$, which is considered as a branch cover of $mathbb{CP}^2$ with respect to a generic projection. The surface has a natural Galois cover with Galois group $S_5$. In this paper, we deal with the fundamental g roups of Galois covers of degree $5$ surfaces that degenerate to nice plane arrangements; each of them is a union of five planes such that no three planes meet in a line.
142 - Benson Farb , Jesse Wolfson 2018
We develop the theory of resolvent degree, introduced by Brauer cite{Br} in order to study the complexity of formulas for roots of polynomials and to give a precise formulation of Hilberts 13th Problem. We extend the context of this theory to enumera tive problems in algebraic geometry, and consider it as an intrinsic invariant of a finite group. As one application of this point of view, we prove that Hilberts 13th Problem, and his Sextic and Octic Conjectures, are equivalent to various enumerative geometry problems, for example problems of finding lines on a smooth cubic surface or bitangents on a smooth planar quartic.
We study triple covers of K3 surfaces, following Mirandas theory of triple covers. We relate the geometry of the covering surfaces with the properties of both the branch locus and the Tschirnhausen vector bundle. In particular, we classify Galois tri ple covers computing numerical invariants of the covering surface and of its minimal model. We provide examples of non Galois triple covers, both in the case in which the Tschirnhausen bundle splits into the sum of two line bundles and in the case in which it is an indecomposable rank 2 vector bundle. We provide a criterion to construct rank 2 vector bundles on a K3 surface $S$ which determine a non-Galois triple cover of $S$. The examples presented are in any admissible Kodaira dimension and in particular we provide the constructions of irregular covers of K3 surfaces and of surfaces with geometrical genus equal to 2 whose transcendental Hodge structure splits in the sum of two Hodge structures of K3 type.
145 - Rong Du , Yun Gao 2012
In this paper, we classified the surfaces whose canonical maps are abelian covers over $mathbb{P}^2$. Moveover, we construct a new Campedelli surface with fundamental group $mathbb{Z}_2^{oplus 3}$ and give defining equations for Persssons surface and Tans surfaces with odd canonical degrees explicitly.
176 - Fabrizio Catanese 2016
We consider a family of surfaces of general type $S$ with $K_S$ ample, having $K^2_S = 24, p_g (S) = 6, q(S)=0$. We prove that for these surfaces the canonical system is base point free and yields an embedding $Phi_1 : S rightarrow mathbb{P}^5$. Th is result answers a question posed by G. and M. Kapustka. We discuss some related open problems, concerning also the case $p_g(S) = 5$, where one requires the canonical map to be birational onto its image.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا