Quantization of canonical cones of algebraic curves

The Tangent Cones at Double points of Prym-Canonical Divisors of Curves of genus 7

Let η be a line bundle on a smooth curve X with η^2=0 such that π_η, the double covering induced by η is an etale morphism. Assume also that X_η be the Prym-canonical model of X associated to K_X.η and Q is a rank 4 quadric containing X_η. After stablishing the projective normality of the prym-canonical models of curves X with Clifford index 2, we obtain in this paper a sufficient condition for...

Rational Parametrizations of Algebraic Curves Using a Canonical Divisor

For an algebraic curve C with genus 0 the vector space L(D) where D is a divisor of degree 2 gives rise to a bijective morphism g from C to a conic C 2 in the projective plane. We present an algorithm that uses an integral basis for computing L(D) for a suitably chosen D. The advantage of an integral basis is that it contains all the necessary information about the singularities, so once the in...

Algebraic Cones

A characterization of algebraic cones in terms of actions of the onedimensional multiplicative algebraic monoid Mm and the algebraic group Gm are given. This note answers a question of K. Adjamagbo asked in [A]. Below all algebraic varieties are taken over an algebraically closed field k. An irreducible algebraic variety X is called a cone if X is affine and its coordinate algebra k[X ] admits ...

Quantization of Classical Curves

We discuss the relation between quantum curves (defined as solutions of equation [P,Q] = ~, where P,Q are ordinary differential operators) and classical curves. We illustrate this relation for the case of quantum curve that corresponds to the (p, q)minimal model coupled to 2D gravity.

Canonical Barriers on Convex Cones