Indecomposable sheaves on the weighted projective line (2,2,n) are bijectively drawn as skew-curves on a symmetric cylinder, with pseudo-triangulations corresponding exactly to tilting sheaves and flips to mutations.
Geometric model for vector bundles via infinite marked strips
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We present a geometric model for the category of vector bundles over the weighted projective line of type (2,2,n). This model is based on the orbit space of an infinite marked strip under a specific group action. We establish a bijection between indecomposable bundles and orbits of line segments on the strip, which yields geometric interpretations for various aspects, including the Picard group action, vector bundle duality, dimension of extension group, projective cover and injective hull of extension bundle, etc.
citation-role summary
background 1
citation-polarity summary
fields
math.RT 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Geometric-combinatorial approaches to tilting theory for weighted projective lines
Indecomposable sheaves on the weighted projective line (2,2,n) are bijectively drawn as skew-curves on a symmetric cylinder, with pseudo-triangulations corresponding exactly to tilting sheaves and flips to mutations.