scholarly journals The irreducible components of the moduli space of dihedral covers of algebraic curves

2015 ◽  
Vol 9 (4) ◽  
pp. 1185-1229 ◽  
Author(s):  
Fabrizio Catanese ◽  
Michael Lönne ◽  
Fabio Perroni
Keyword(s):  
Moduli Space ◽  
Algebraic Curves ◽  
Irreducible Components

scholarly journals Moduli of Space Sheaves with Hilbert Polynomial 4m+ 1

2018 ◽  
Vol 61 (2) ◽  
pp. 328-345 ◽  
Author(s):  
Mario Maican
Keyword(s):  
Euler Characteristic ◽  
Moduli Space ◽  
Elementary Proof ◽  
Hilbert Polynomial ◽  
Space Curves ◽  
Irreducible Components

AbstractWe investigate the moduli space of sheaves supported on space curves of degree and having Euler characteristic 1. We give an elementary proof of the fact that this moduli space consists of three irreducible components.

scholarly journals ON THE GEOMETRY OF MODULI SPACES OF COHERENT SYSTEMS ON ALGEBRAIC CURVES

2007 ◽  
Vol 18 (04) ◽  
pp. 411-453 ◽  
Author(s):  
S. B. BRADLOW ◽  
O. GARCÍA-PRADA ◽  
V. MERCAT ◽  
V. MUÑOZ ◽  
P. E. NEWSTEAD
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Algebraic Curves ◽  
Homotopy Groups ◽  
Coherent System ◽  
Coherent Systems ◽  
Picard Groups ◽  
Algebraic Vector ◽  
The Stability ◽  
Almost All

Let C be an algebraic curve of genus g ≥ 2. A coherent system on C consists of a pair (E,V), where E is an algebraic vector bundle over C of rank n and degree d and V is a subspace of dimension k of the space of sections of E. The stability of the coherent system depends on a parameter α. We study the geometry of the moduli space of coherent systems for different values of α when k ≤ n and the variation of the moduli spaces when we vary α. As a consequence, for sufficiently large α, we compute the Picard groups and the first and second homotopy groups of the moduli spaces of coherent systems in almost all cases, describe the moduli space for the case k = n - 1 explicitly, and give the Poincaré polynomials for the case k = n - 2. In an appendix, we describe the geometry of the "flips" which take place at critical values of α in the simplest case, and include a proof of the existence of universal families of coherent systems when GCD (n,d,k) = 1.

On the structure of the Whittaker sublocus of the moduli space of algebraic curves

2006 ◽  
Vol 136 (2) ◽  
pp. 337-346
Author(s):  
Ernesto Girondo ◽  
Gabino González-Diez
Keyword(s):  
Differential Equations ◽  
Algebraic Equation ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Algebraic Curves ◽  
Hyperelliptic Curves ◽  
Teichmuller Theory ◽  
Compactness Result ◽  
Teichmüller Theory ◽  
Fuchsian Differential Equations

We prove the compactness of the Whittaker sublocus of the moduli space of Riemann surfaces (complex algebraic curves). This is the subset of points representing hyperelliptic curves that satisfy Whittaker's conjecture on the uniformization of hyperelliptic curves via the monodromy of Fuchsian differential equations. In the last part of the paper we devote our attention to the statement made by R. A. Rankin more than 40 years ago, to the effect that the conjecture ‘has not been proved for any algebraic equation containing irremovable arbitrary constants’. We combine our compactness result with other facts about Teichmüller theory to show that, in the most natural interpretations of this statement we can think of, this result is, in fact, impossible.

ON THE CONNECTEDNESS OF THE LOCUS OF REAL ELLIPTIC-HYPERELLIPTIC RIEMANN SURFACES

2009 ◽  
Vol 20 (08) ◽  
pp. 1069-1080 ◽  
Author(s):  
JOSÉ A. BUJALANCE ◽  
ANTONIO F. COSTA ◽  
ANA M. PORTO
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Algebraic Curves ◽  
Orbit Space ◽  
Previous Article ◽  
Connected Components ◽  
Hyperelliptic Involution ◽  
Hyperelliptic Surfaces ◽  
Genus One

A Riemann surface X of genus g > 2 is elliptic-hyperelliptic if it admits a conformal involution h such that the orbit space X/〈h〉 has genus one. This elliptic-hyperelliptic involution h is unique for g > 5 [1]. In a previous article [3], we established the non-connectedness of the subspace [Formula: see text] of real elliptic-hyperelliptic algebraic curves in the moduli space [Formula: see text] of Riemann surfaces of genus g, when g is even and > 5. In this paper we improve this result and give a complete answer to the connectedness problem of the space [Formula: see text] of real elliptic-hyperelliptic surfaces of genus > 5: we show that [Formula: see text] is connected if g is odd and has exactly two connected components if g is even; in both cases the closure [Formula: see text] of [Formula: see text] in the compactified moduli space [Formula: see text] is connected.

scholarly journals The Supersingular Locus of the Shimura Variety for GU(1, s)

2010 ◽  
Vol 62 (3) ◽  
pp. 668-720 ◽  
Author(s):  
Inken Vollaard
Keyword(s):  
Complete Intersection ◽  
Moduli Space ◽  
Unitary Group ◽  
Shimura Variety ◽  
Incidence Relation ◽  
Irreducible Components ◽  
Reduction Modulo ◽  
Tits Building ◽  
Divisible Groups ◽  
Dieudonne Theory

AbstractIn this paper we study the supersingular locus of the reduction modulopof the Shimura variety for GU(1,s) in the case of an inert primep. Using Dieudonné theory we define a stratification of the corresponding moduli space ofp-divisible groups. We describe the incidence relation of this stratification in terms of the Bruhat–Tits building of a unitary group.In the case of GU(1, 2), we show that the supersingular locus is equidimensional of dimension 1 and is of complete intersection. We give an explicit description of the irreducible components and their intersection behaviour.

scholarly journals ON THE MONODROMY AND GALOIS GROUP OF CONICS LYING ON HEISENBERG INVARIANT QUARTIC K3 SURFACES

2019 ◽  
Vol 62 (3) ◽  
pp. 640-660
Author(s):  
FLORIAN BOUYER
Keyword(s):  
Galois Group ◽  
Moduli Space ◽  
Monodromy Group ◽  
K3 Surfaces ◽  
K3 Surface ◽  
Field Of Definition ◽  
Irreducible Components ◽  
Definition Of

AbstractIn [5], Eklund showed that a general (ℤ/2ℤ)4 -invariant quartic K3 surface contains at least 320 conics. In this paper, we analyse the field of definition of those conics as well as their Monodromy group. As a result, we prove that the moduli space of (ℤ/2ℤ)4-invariant quartic K3 surface with a certain marked conic has 10 irreducible components.

scholarly journals RATIONAL FAMILIES OF VECTOR BUNDLES ON CURVES

2004 ◽  
Vol 15 (01) ◽  
pp. 13-45 ◽  
Author(s):  
ANA-MARIA CASTRAVET
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Rational Curves ◽  
Complex Curve ◽  
Stable Vector Bundles ◽  
Irreducible Components ◽  
Rationally Connected ◽  
Rank 2 ◽  
Rank 2 Vector Bundles

Let C be a smooth projective complex curve of genus g≥2 and let M be the moduli space of rank 2, stable vector bundles on C, with fixed determinant of degree 1. For any k≥1, we find all the irreducible components of the space of rational curves on M, of degree k. In particular, we find the maximal rationally connected fibrations of these components. We prove that there is a one-to-one correspondence between moduli spaces of rational curves on M and moduli spaces of rank 2 vector bundles on ℙ1×C.

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