Let $E$ be a stable bundle on a smooth curve of genus $g$. Assume $\chi(E)\leq 0$ or equivalently, $E$ has slope $\leq g-1$. Is there a line bundle $L$ of degree 0 such that $H^0(E\otimes L)=0$ ?
2026-03-25 09:48:34.1774432114
Stable vector bundles on an algebraic curve
52 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in ALGEBRAIC-GEOMETRY
- How to see line bundle on $\mathbb P^1$ intuitively?
- Jacobson radical = nilradical iff every open set of $\text{Spec}A$ contains a closed point.
- Is $ X \to \mathrm{CH}^i (X) $ covariant or contravariant?
- An irreducible $k$-scheme of finite type is "geometrically equidimensional".
- Global section of line bundle of degree 0
- Is there a variant of the implicit function theorem covering a branch of a curve around a singular point?
- Singular points of a curve
- Find Canonical equation of a Hyperbola
- Picard group of a fibration
- Finding a quartic with some prescribed multiplicities
Related Questions in CURVES
- Studying regular space curves when restricted to two differentiable functions
- The problem in my proof that if $\beta(s)=\alpha(-s)$ then the torsions of the curves satisfies $\tau_{\beta}(s)=-\tau_{\alpha}(-s)$
- Given a circle, can i assume that the point where all the normals went thought and the point where all the tangents are equidistants are the same?
- Function determining temperature of points along a curve (find local maxima temp & local minima temp)
- Reference for $L$-functions of curves
- About the Green's Theorem
- inhomogeneous coordinates to homogeneous coordinates
- Can the relocation of one control point of a NURBS curve be compensated by an adjustment of some weights?
- $\| \gamma'(t) \|$ = constant for all $t$, if and only if $\gamma''(t)$ is normal to the tangent vector space for all $t$.
- proving that a curve with constant curvature contained in a sphere its a circle
Related Questions in VECTOR-BUNDLES
- Compute Thom and Euler class
- Confusion about relationship between operator $K$-theory and topological $K$-theory
- Bott and Tu exercise 6.5 - Reducing the structure group of a vector bundle to $O(n)$
- Why is the index of a harmonic map finite?
- Scheme theoretic definition of a vector bundle
- Is a disjoint union locally a cartesian product?
- fiber bundles with both base and fiber as $S^1$.
- Is quotient bundle isomorphic to the orthogonal complement?
- Can We understand Vector Bundles as pushouts?
- Connection on a vector bundle in terms of sections
Related Questions in ALGEBRAIC-CURVES
- Singular points of a curve
- Finding a quartic with some prescribed multiplicities
- Tangent lines of a projective curve
- Value of $t$ for which a curve has singular points.
- Reference for $L$-functions of curves
- Bézout's theorem for intersection of curves
- Curves of genus 0
- Multiplicity of singular points in a curve.
- Intersection of a quartic and conics.
- Rational points on conics over fields of dimension 1
Related Questions in ALGEBRAIC-VECTOR-BUNDLES
- Degree of sub sheaf of locally free sheaf is bounded
- Grothendieck group of a smooth complex projective curve
- chern class of bundle in Blochs "Cycles on arithmetic schemes"
- Pushforward of a line bundle along a finite morphism of curves
- What is transition function of scheme theoretic vector bundle ??
- Line bundles correspoding to a hyperplane
- On the ring structure of $K_0$ of the punctured spectrum of a regular local ring
- Cohen-Macaulay sheaves in Picard group of Cohen-Macaulay schemes
- "Transition morphism" of fiber bundle
- Where do I find this article?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?