scholarly journals Instanton sheaves and representations of quivers

2020 ◽  
Vol 63 (4) ◽  
pp. 984-1004
Author(s):  
M. Jardim ◽  
D. D. Silva
Keyword(s):  
Moduli Space ◽  
Stability Parameter ◽  
Quiver Representation ◽  
Stability Parameters ◽  
Representations Of Quivers ◽  
Rank 2 ◽  
Low Charge

AbstractWe study the moduli space of rank 2 instanton sheaves on ℙ3 in terms of representations of a quiver consisting of three vertices and four arrows between two pairs of vertices. Aiming at an alternative compactification for the moduli space of instanton sheaves, we show that for each rank 2 instanton sheaf, there is a stability parameter θ for which the corresponding quiver representation is θ-stable (in the sense of King), and that the space of stability parameters has a non-trivial wall-and-chamber decomposition. Looking more closely at instantons of low charge, we prove that there are stability parameters with respect to which every representation corresponding to a rank 2 instanton sheaf of charge 2 is stable and provide a complete description of the wall-and-chamber decomposition for representation corresponding to a rank 2 instanton sheaf of charge 1.

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 EXTENSIONS AND RANK-2 VECTOR BUNDLES ON IRREDUCIBLE NODAL CURVES

2005 ◽  
Vol 16 (10) ◽  
pp. 1081-1118
Author(s):  
D. ARCARA
Keyword(s):  
Moduli Space ◽  
Vector Bundles ◽  
Rational Map ◽  
Nodal Curves ◽  
Nodal Curve ◽  
Stable Vector Bundles ◽  
Rank 2 ◽  
Rank 2 Vector Bundles

We generalize Bertram's work on rank two vector bundles to an irreducible projective nodal curve C. We use the natural rational map [Formula: see text] defined by [Formula: see text] to study a compactification [Formula: see text] of the moduli space [Formula: see text] of semi-stable vector bundles of rank 2 and determinant L on C. In particular, we resolve the indeterminancy of ϕL in the case deg L = 3,4 via a sequence of three blow-ups with smooth centers.

scholarly journals A note on 1-cycles on the moduli space of rank-2 bundles over a curve

2019 ◽  
Vol 357 (2) ◽  
pp. 209-211
Author(s):  
Duo Li ◽  
Yinbang Lin ◽  
Xuanyu Pan
Keyword(s):  
Moduli Space ◽  
Rank 2 ◽  
Rank 2 Bundles

STABLE RANK-2 BUNDLES ON CALABI–YAU MANIFOLDS

2003 ◽  
Vol 14 (10) ◽  
pp. 1097-1120 ◽  
Author(s):  
WEI-PING LI ◽  
ZHENBO QIN
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Double Cover ◽  
Stable Rank ◽  
Chern Classes ◽  
Canonical Divisor ◽  
Rank 2 ◽  
Stable Sheaves ◽  
Rank 2 Bundles ◽  
Calabi Yau Manifolds

In this paper, we apply the technique of chamber structures of stability polarizations to construct the full moduli space of rank-2 stable sheaves with certain Chern classes on Calabi–Yau manifolds which are anti-canonical divisor of ℙ1×ℙn or a double cover of ℙ1×ℙn. These moduli spaces are isomorphic to projective spaces. As an application, we compute the holomorphic Casson invariants defined by Donaldson and Thomas.

Moduli of Rank 2 Stable Bundles and Hecke Curves

2016 ◽  
Vol 59 (4) ◽  
pp. 865-877
Author(s):  
Sarbeswar Pal
Keyword(s):  
Moduli Space ◽  
Vector Bundles ◽  
Short Note ◽  
Equivalence Classes ◽  
Complex Numbers ◽  
Stable Bundles ◽  
Smooth Projective Curve ◽  
Stable Vector Bundles ◽  
Arbitrary Genus ◽  
Rank 2

AbstractLet X be a smooth projective curve of arbitrary genus g > 3 over the complex numbers. In this short note we will show that the moduli space of rank 2 stable vector bundles with determinant isomorphic to Lx , where Lx denotes the line bundle corresponding to a point x ∊ X, is isomorphic to a certain variety of lines in the moduli space of S-equivalence classes of semistable bundles of rank 2 with trivial determinant.

scholarly journals Shear frame stability parameters for large-scale avalanche forecasting

1993 ◽  
Vol 18 ◽  
pp. 268-273 ◽  
Author(s):  
J.B. Jamieson ◽  
C.D. Johnston
Keyword(s):  
Shear Strength ◽  
Large Scale ◽  
Normal Load ◽  
Meteorological Data ◽  
Stability Index ◽  
Stability Parameter ◽  
Stability Parameters ◽  
Avalanche Forecasting ◽  
Study Plot ◽  
Shear Frame

During the winters of 1990, 1991 and 1992, a field study of stability parameters for forecasting slab avalanches was conducted in the Cariboo and Monashee mountains of western Canada. In a level study plot at 1900 m and on nearby slopes, the shear strength of the weak snowpack layer judged most likely to cause slab avalanches was measured with a 0.025 m2 shear frame and a force gauge. Based on the ratio of shear strength to stress due to the snow load overlying the weak layer, a simple stability parameter and a more theoretically based stability index which corrects the strength for normal load were calculated. These stability parameters are compared with avalanche activity reported for the same day within approximately 30 km of the study plot. Each stability parameter is assessed on the basis of the number of days that it successfully predicted one or more potentially harmful avalanches and the number of days that it successfully predicted no potentially harmful avalanches. Both parameters predicted correctly on at least 75% of the 70 days they were evaluated. The simpler empirical stability parameter worked as well as the one that corrects strength for normal load. For large-scale forecasting of dry-snow slab avalanches, shear frame stability parameters appear to be a useful addition to meteorological data, snowpack observations and slope tests.

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