17,578 research outputs found
Enumerative geometry of dormant opers
The purpose of the present paper is to develop the enumerative geometry of
dormant -opers for a semisimple algebraic group . In the present paper,
we construct a compact moduli stack admitting a perfect obstruction theory by
introducing the notion of a dormant faithful twisted -oper (or a
"-do'per" for short. Moreover, a semisimple d TQFT (= -dimensional
topological quantum field theory) counting the number of -do'pers is
obtained by means of the resulting virtual fundamental class. This d TQFT
gives an analogue of the Witten-Kontsevich theorem describing the intersection
numbers of psi classes on the moduli stack of -do'pers.Comment: 64 pages, the title is changed, some mistakes are correcte
On the cuspidalization problem for hyperbolic curves over finite fields
In this paper, we study some group-theoretic constructions associated to
arithmetic fundamental groups of hyperbolic curves over finite fields. One of
the main results of this paper asserts that any Frobenius-preserving
isomorphism between the geometrically pro- fundamental groups of hyperbolic
curves with one given point removed induces an isomorphism between the
geometrically pro- fundamental groups of the hyperbolic curves obtained by
removing other points. Finally, we apply this result to obtain results
concerning certain cuspidalization problems for fundamental groups of (not
necessarily proper) hyperbolic curves over finite fields.Comment: 44 pages, to appear in Kyoto Journal of Mathematic
Duality for dormant opers
In the present paper, we prove that on a fixed pointed stable curve of
characteristic , there exists a duality between dormant
-opers () and dormant
-opers. Also, we prove that there exists a unique (up to
isomorphism) dormant -oper on a fixed pointed stable
curve of characteristic .Comment: 41 page
- β¦