scholarly journals Moduli Spaces of Representations of Special Biserial Algebras

2018 ◽  
Vol 2020 (2) ◽  
pp. 403-421 ◽  
Author(s):  
Andrew T Carroll ◽  
Calin Chindris ◽  
Ryan Kinser ◽  
Jerzy Weyman
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Projective Spaces ◽  
Special Biserial Algebras ◽  
Irreducible Components ◽  
Special Biserial Algebra

Abstract We show that the irreducible components of any moduli space of semistable representations of a special biserial algebra are always isomorphic to products of projective spaces of various dimensions. This is done by showing that irreducible components of varieties of representations of special biserial algebras are isomorphic to irreducible components of products of varieties of circular complexes and therefore normal, allowing us to apply recent results of the second and third authors on moduli spaces.

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.

MODULI SPACES OF STABLE BUNDLES ON K3 FIBERED CALABI–YAU THREEFOLDS

2003 ◽  
Vol 05 (01) ◽  
pp. 119-126 ◽  
Author(s):  
TOHRU NAKASHIMA
Keyword(s):  
Moduli Spaces ◽  
Projective Spaces ◽  
Stable Rank ◽  
Stable Bundles ◽  
Irreducible Components

In this paper we study stable rank two bundles on a Calabi–Yau threefold. For hypersurfaces in a ℙ3-bundle over ℙ1, we show that their moduli spaces have irreducible components which are birational to projective spaces.

scholarly journals Moduli Spaces of Point Configurations and Plane Curve Counts

2019 ◽  
Author(s):  
Markus Reineke ◽  
Thorsten Weist
Keyword(s):  
Recurrence Relation ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Plane Curve ◽  
Projective Spaces ◽  
Rational Curves ◽  
Euler Characteristics ◽  
Point Configurations

Abstract We identify certain Gromov–Witten invariants counting rational curves with given incidence and tangency conditions with the Euler characteristics of moduli spaces of point configurations in projective spaces. On the Gromov–Witten side, S. Fomin and G. Mikhalkin established a recurrence relation via tropicalization, which is realized on the moduli space side using Donaldson–Thomas invariants of subspace quivers.

scholarly journals Geometric Manin’s conjecture and rational curves

2019 ◽  
Vol 155 (5) ◽  
pp. 833-862 ◽  
Author(s):  
Brian Lehmann ◽  
Sho Tanimoto
Keyword(s):  
Growth Rate ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Counting Function ◽  
Rational Curves ◽  
Fano Variety ◽  
Complex Numbers ◽  
Number Of Components ◽  
Irreducible Components ◽  
Manin’S Conjecture

Let$X$be a smooth projective Fano variety over the complex numbers. We study the moduli space of rational curves on$X$using the perspective of Manin’s conjecture. In particular, we bound the dimension and number of components of spaces of rational curves on$X$. We propose a geometric Manin’s conjecture predicting the growth rate of a counting function associated to the irreducible components of these moduli spaces.

Hitchin pairs on reducible curves

2018 ◽  
Vol 29 (03) ◽  
pp. 1850015 ◽  
Author(s):  
Usha N. Bhosle
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Disjoint Union ◽  
Higgs Bundles ◽  
Projective Curve ◽  
Birational Morphism ◽  
Smooth Curves ◽  
Irreducible Components ◽  
Proper Map ◽  
The Relationship

We define semistable generalized parabolic Hitchin pairs (GPH) on a disjoint union [Formula: see text] of integral smooth curves and construct their moduli spaces. We define a Hitchin map on the moduli space of GPH and show that it is a proper map. We construct moduli spaces of semistable Hitchin pairs on a reducible projective curve [Formula: see text]. When [Formula: see text] is the normalization of [Formula: see text], we give a birational morphism [Formula: see text] from the moduli space [Formula: see text] of good GPH on [Formula: see text] to the moduli space [Formula: see text] of Hitchin pairs on [Formula: see text] and show that the Hitchin map on [Formula: see text] induces a proper Hitchin map on [Formula: see text]. We determine the fibers of the Hitchin maps. We study the relationship between representations of the (topological) fundamental group of [Formula: see text] and Higgs bundles on [Formula: see text]. We show that if all the irreducible components of [Formula: see text] are smooth, then the Hitchin map is defined on the entire moduli space [Formula: see text].

scholarly journals On the Voevodsky motive of the moduli space of Higgs bundles on a curve

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Victoria Hoskins ◽  
Simon Pepin Lehalleur
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Characteristic Zero ◽  
Rational Point ◽  
Triangulated Category ◽  
Higgs Bundles ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
De Rham

AbstractWe study the motive of the moduli space of semistable Higgs bundles of coprime rank and degree on a smooth projective curve C over a field k under the assumption that C has a rational point. We show this motive is contained in the thick tensor subcategory of Voevodsky’s triangulated category of motives with rational coefficients generated by the motive of C. Moreover, over a field of characteristic zero, we prove a motivic non-abelian Hodge correspondence: the integral motives of the Higgs and de Rham moduli spaces are isomorphic.

scholarly journals EXTREMAL CASES OF RAPOPORT–ZINK SPACES

2021 ◽  
pp. 1-56
Author(s):  
Ulrich Görtz ◽  
Xuhua He ◽  
Michael Rapoport
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Complete List ◽  
Qualitative Properties ◽  
Model Case ◽  
Divisible Groups

Abstract We investigate qualitative properties of the underlying scheme of Rapoport–Zink formal moduli spaces of p-divisible groups (resp., shtukas). We single out those cases where the dimension of this underlying scheme is zero (resp., those where the dimension is the maximal possible). The model case for the first alternative is the Lubin–Tate moduli space, and the model case for the second alternative is the Drinfeld moduli space. We exhibit a complete list in both cases.

scholarly journals THE HYPERELLIPTIC THETA MAP AND OSCULATING PROJECTIONS

2020 ◽  
pp. 1-23
Author(s):  
MICHELE BOLOGNESI ◽  
NÉSTOR FERNÁNDEZ VARGAS
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Hyperelliptic Curve ◽  
Geometric Description ◽  
Birational Model ◽  
Rank 2 ◽  
Semistable Vector Bundles ◽  
Ramification Locus

Abstract Let C be a hyperelliptic curve of genus $g \geq 3$ . In this paper, we give a new geometric description of the theta map for moduli spaces of rank 2 semistable vector bundles on C with trivial determinant. In order to do this, we describe a fibration of (a birational model of) the moduli space, whose fibers are GIT quotients $(\mathbb {P}^1)^{2g}//\text {PGL(2)}$ . Then, we identify the restriction of the theta map to these GIT quotients with some explicit degree 2 osculating projection. As a corollary of this construction, we obtain a birational inclusion of a fibration in Kummer $(g-1)$ -varieties over $\mathbb {P}^g$ inside the ramification locus of the theta map.

scholarly journals A note on moduli spaces of conformal classes for flat tori of higher dimension and on their conformal multiplication

2021 ◽  
Author(s):  
Anna Gori ◽  
Alberto Verjovsky ◽  
Fabio Vlacci
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Abelian Varieties ◽  
Complex Multiplication ◽  
Higher Dimension ◽  
Geometric Constructions ◽  
Flat Torus ◽  
Flat Tori

AbstractMotivated by the theory of complex multiplication of abelian varieties, in this paper we study the conformality classes of flat tori in $${\mathbb {R}}^{n}$$ R n and investigate criteria to determine whether a n-dimensional flat torus has non trivial (i.e. bigger than $${\mathbb {Z}}^{*}={\mathbb {Z}}{\setminus }\{0\}$$ Z ∗ = Z \ { 0 } ) semigroup of conformal endomorphisms (the analogs of isogenies for abelian varieties). We then exhibit several geometric constructions of tori with this property and study the class of conformally equivalent lattices in order to describe the moduli space of the corresponding tori.

scholarly journals On the boundary of the moduli spaces of log Hodge structures: Triviality of the torsor

2010 ◽  
Vol 198 ◽  
pp. 173-190 ◽  
Author(s):  
Tatsuki Hayama
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Hodge Structures

AbstractThis paper examines the moduli spaces of log Hodge structures introduced by Kato and Usui. This moduli space is a partial compactification of a discrete quotient of a period domain. This paper treats the following two cases: (A) where the period domain is Hermitian symmetric, and (B) where the Hodge structures are of the mirror quintic type. Especially it addresses a property of the torsor.

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