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The stable reduction theorem was proved by Grothendieck for Abelian varieties and subsequently by Deligne and Mumford for projective curves.
For smooth families of projective algebraic curves, we extend the notion of intersection pairing of metrized line bundles to a pairing on line bundles with flat relative connections. In this setting, ...
Abstract: Given a non-rational real space curve and a tolerance $\epsilon>0$, we present an algorithm to approximately parametrize the curve. The algorithm checks whether a planar projection of the sp...
The Schur function expansion of Sato-Segal-Wilson KP τ -functions is reviewed. The case of τ -functions related to algebraic curves of arbitrary genus is studied in detail. Explicit expressions for t...
The Schur function expansion of Sato-Segal-Wilson KP τ -functions is reviewed. The case of τ -functions related to algebraic curves of arbitrary genus is studied in detail.
Algebraic varieties and curves arising in Birkhoff strata of the Sato Grassmannian Gr${^{(2)}}$ are studied. It is shown that the big cell $\Sigma_0$ contains the tower of families of the normal rati...
We prove irreducibility for the space of cyclic covers of fixed numerical type between smooth projective curves, and also for the space of cyclic covers of prime order and of fixed numerical-combinato...
In this work we study a problem about analytic continuation along parallel algebraic curves
In this paper, we develop the theory of flashes of an algebraic curve. We show that the theory is birationally invariant in a sense which we will make more precise below. We also show how the theory p...
For any d\ge 5, I constructed infinitely many pairwise smoothly non-equivalent surfaces F\subset\Cp{2} homeomorphic to a non-singular algebraic curve of degree d, realizing the same homology class as ...
We use a combination of both algebraic and numerical techniques to construct a $C^1$-continuous, piecewise $(m,n)$ rational $\epsilon$-approximation of a real algebraic plane curve of degree $d$. ...
In this paper, I have considered some problems of algebraic curves in some constructive way, especially, I give an algorithm for determining whether two given smooth plane curves are isomorphic and fi...
An algorithm is proposed to give a global approximation of an implicit real plane algebraic curve with rational quadratic B-spline curves. The algorithm consists of four steps: topology determination,...
In this paper, by using the concept of resolvents of a prime ideal introduced by Ritt, we give methods for constructing a hypersurface which is birational to a given irreducible variety and birational...

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