MAT 614 Curves on Algebraic Varieties
نویسنده
چکیده
(f) Explicitly verify that the the 5 global sections above generate the invertible sheaf OP2(2)|X(−C) at every point of X. Therefore there is a unique morphism φ : X → P such that φOP4(1) equals OP2(2)|X(−C) and the pullback of the homogeneous coordinates are the 5 sections above. (g) Also verify that y0, y1, y2, y3 are identically zero on the line L. Therefore φ contracts L to the point p = [0, 0, 0, 0, 1].
منابع مشابه
Geometry of Rational Curves on Algebraic Varieties
Geometry of Rational Curves on Algebraic Varieties
متن کاملAlgebraic description of Jacobians isogeneous to certain Prym varieties with polarization (1,2)∗
For a class of non-hyperelliptic genus 3 curves C which are 2-fold coverings of elliptic curves E, we give an explicit algebraic description of all birationally nonequivalent genus 2 curves whose Jacobians are degree 2 isogeneous to the Prym varieties associated to such coverings. Our description is based on previous studies of Prym varieties with polarization (1,2) in connection with separatio...
متن کاملCodes on Varieties as Codes on Curves
The discovery of algebraic geometric codes constructed on curves led to generalising this construction on higher dimensional varieties. In this paper, we use a theorem of B. Poonen to show that the codes obtained from higher dimensional varieties can be realised as codes on curves. One of the important consequences of this result is that the search for good codes on varieties that beat the exis...
متن کاملMAXIMAL PRYM VARIETY AND MAXIMAL MORPHISM
We investigated maximal Prym varieties on finite fields by attaining their upper bounds on the number of rational points. This concept gave us a motivation for defining a generalized definition of maximal curves i.e. maximal morphisms. By MAGMA, we give some non-trivial examples of maximal morphisms that results in non-trivial examples of maximal Prym varieties.
متن کاملGeometry of Obstructed Equisingular Families of Algebraic Curves and Hypersurfaces
One of the main achievements of the algebraic geometry of the 20th century was to realize that it is fruitful not only to study algebraic varieties by themselves but also in families. That means that one should consider the space classifying all varieties with given properties. These spaces are called moduli spaces. The advantage of algebraic geometry is that many times those spaces are themsel...
متن کامل