Given a complex surface $X$ and $D$ a smooth curve on $X$, there is an associated line bundle $L(D)$ over $X$. Is there always a global section $s\in H^0(X,L(X))$, s.t. $s$ is just vanishing on $D$?
2026-03-26 03:12:15.1774494735
Existence of a global section of $L(D)$ vanishing on $D$.
45 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in COMPLEX-GEOMETRY
- Numerable basis of holomporphic functions on a Torus
- Relation between Fubini-Study metric and curvature
- Hausdorff Distance Between Projective Varieties
- What can the disk conformally cover?
- Some questions on the tangent bundle of manifolds
- Inequivalent holomorphic atlases
- Reason for Graphing Complex Numbers
- Why is the quintic in $\mathbb{CP}^4$ simply connected?
- Kaehler Potential Convexity
- I want the pullback of a non-closed 1-form to be closed. Is that possible?
Related Questions in LINE-BUNDLES
- How to see line bundle on $\mathbb P^1$ intuitively?
- Global section of line bundle of degree 0
- Picard group of a fibration
- Hyperplane line bundle really defined by some hyperplane
- Understanding line bundles on $\mathbb{P}_k^1$ using transition functions
- Very ample line bundle on a projective curve
- Local computation of the curvature form of a line bundle
- $P$ is a branching point of the elliptic curve $(E, P)$
- Why does a globally generated invertible sheaf admit a global section not vanishing on any irreducible component?
- Global section $s$ of ample line bundle such that $X_s$ is everywhere dense
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?