21 окт. 2017 г. · I'm currently working my way through Foundations of Projective Geometry by Hartshorne, and he states the axioms characterizing an affine plane as:

2 июл. 2014 г. · "Foundations of Projective Geometry" by Hartshorne says the following: The completion of the affine plane of four points is a projective ...

11 февр. 2015 г. · In chapter II of Hartshorne, theorem 4.9 shows that every projective morphism is proper, using the valuative criterion for properness. I ...

7 авг. 2023 г. · Fix coordinates so that P is [0:⋯:0:1]. Then the formula for the projection map Pn+1∖{P}→Pn is [x0:⋯:xn:xn+1]↦[x0:⋯:xn].

10 окт. 2014 г. · First of all, the notation Hartshorne uses is a bit confusing: by I(Y)S(Y)(xi) Hartshorne means the ideal (I(Y)⋅S(Y)xi)∩S(Y)(xi) (see here).

23 мар. 2016 г. · Suppose that we have a principal divisor D on X. I want to show that there is a rational function f on Pn so that D=(f)∩X (i.e the restriction ...

20 нояб. 2018 г. · In Hartshorne's Algebraic Geometry, page 103, a morphism f:X→Y is said to be projective if it factors as a closed immersion X→PnY followed ...

14 дек. 2018 г. · On an exercise in section 4 of Chapter I from Hartshorne's Algebraic Geometry ... It is about exercise 4.9: Let X be a projective variety of ...

4 дек. 2016 г. · Let X be a projective variety of dimension r in Pn with n≥r+2. Show that for suitable choice of P∉X, and a linear ...

30 июл. 2020 г. · Understanding Hartshorne's proof that every projective morphism is proper. 2 · Invariance under change of cohordinates cohomology projective ...