Projective variety (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Projective variety" in English language version.

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Hartshorne 1977, Section II.5 Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157
cf. the proof of Hartshorne 1977, Ch II, Theorem 7.1 Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157
Grothendieck & Dieudonné 1961, 5.6 Grothendieck, Alexandre; Dieudonné, Jean (1961). "Éléments de géométrie algébrique: II. Étude globale élémentaire de quelques classes de morphismes". Publications Mathématiques de l'IHÉS. 8. doi:10.1007/bf02699291. MR 0217084.
Hartshorne 1977, Ch II. Exercise 4.5 Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157
Hartshorne 1977, Ch. V, Exercise 3.4. (e). Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157
Fulton 1998, Proposition 8.4. Fulton, William (1998), Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge., vol. 2 (2nd ed.), Berlin, New York: Springer-Verlag, ISBN 978-3-540-62046-4, MR 1644323
Hartshorne 1977, Ch. II, Exercise 5.14. (a) Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157
Hartshorne 1977, Ch IV, Exercise 1.7. Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157
Hartshorne 1977, Ch I, Exercise 2.8; this is because the homogeneous coordinate ring of $\mathbb {P} ^{n}$ is a unique factorization domain and in a UFD every prime ideal of height 1 is principal. Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157
Hartshorne 1977, Ch. I, Exercise 4.9. Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157
Fulton 1998, § 4.4. Fulton, William (1998), Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge., vol. 2 (2nd ed.), Berlin, New York: Springer-Verlag, ISBN 978-3-540-62046-4, MR 1644323
This is not difficult:(Hartshorne 1977, Ch III. Lemma 2.10) consider a flasque resolution of ${\mathcal {F}}$ and its zero-extension to the whole projective space. Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157
Hartshorne 1977, Ch III. Theorem 5.2 Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157
Hartshorne 1977, Ch III. Exercise 5.2 Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157
Hartshorne 1977, Ch IV. Theorem 1.3 Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157
Hartshorne 1977, Appendix B. Theorem 3.4. Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157
Hartshorne 1977, Appendix B. Theorem 2.1 Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157
Hartshorne 1977, Ch III. Remark 7.15. Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157
Dolgachev, Igor (1982), "Weighted projective varieties", Group actions and vector fields (Vancouver, B.C., 1981), Lecture Notes in Math., vol. 956, Berlin: Springer, pp. 34–71, CiteSeerX 10.1.1.169.5185, doi:10.1007/BFb0101508, ISBN 978-3-540-11946-3, MR 0704986

books.google.com

Griffiths & Adams 2015, IV. 1. 10. Corollary H Griffiths, Phillip A.; Adams, John Frank (8 March 2015). Topics in Algebraic and Analytic Geometry. (MN-13), Volume 13: Notes From a Course of Phillip Griffiths. Princeton University Press. ISBN 978-1-4008-6926-8.
Griffiths & Adams 2015, IV. 1. 10. Corollary I Griffiths, Phillip A.; Adams, John Frank (8 March 2015). Topics in Algebraic and Analytic Geometry. (MN-13), Volume 13: Notes From a Course of Phillip Griffiths. Princeton University Press. ISBN 978-1-4008-6926-8.

doi.org

Mumford 1999, pg. 82 Mumford, David (1999), The Red Book of Varieties and Schemes: Includes the Michigan Lectures (1974) on Curves and Their Jacobians, Lecture Notes in Mathematics, vol. 1358 (2nd ed.), Springer-Verlag, doi:10.1007/b62130, ISBN 978-3540632931
Mumford 1999, pg. 111 Mumford, David (1999), The Red Book of Varieties and Schemes: Includes the Michigan Lectures (1974) on Curves and Their Jacobians, Lecture Notes in Mathematics, vol. 1358 (2nd ed.), Springer-Verlag, doi:10.1007/b62130, ISBN 978-3540632931
Grothendieck & Dieudonné 1961, 5.6 Grothendieck, Alexandre; Dieudonné, Jean (1961). "Éléments de géométrie algébrique: II. Étude globale élémentaire de quelques classes de morphismes". Publications Mathématiques de l'IHÉS. 8. doi:10.1007/bf02699291. MR 0217084.
Dolgachev, Igor (1982), "Weighted projective varieties", Group actions and vector fields (Vancouver, B.C., 1981), Lecture Notes in Math., vol. 956, Berlin: Springer, pp. 34–71, CiteSeerX 10.1.1.169.5185, doi:10.1007/BFb0101508, ISBN 978-3-540-11946-3, MR 0704986

numdam.org

Grothendieck & Dieudonné 1961, 5.6 Grothendieck, Alexandre; Dieudonné, Jean (1961). "Éléments de géométrie algébrique: II. Étude globale élémentaire de quelques classes de morphismes". Publications Mathématiques de l'IHÉS. 8. doi:10.1007/bf02699291. MR 0217084.

princeton.edu

web.math.princeton.edu

Kollár & Moduli, Ch I. Kollár, János, Book on Moduli of Surfaces

psu.edu

citeseerx.ist.psu.edu

Dolgachev, Igor (1982), "Weighted projective varieties", Group actions and vector fields (Vancouver, B.C., 1981), Lecture Notes in Math., vol. 956, Berlin: Springer, pp. 34–71, CiteSeerX 10.1.1.169.5185, doi:10.1007/BFb0101508, ISBN 978-3-540-11946-3, MR 0704986

upenn.edu

math.upenn.edu

Mumford & Oda 2015, Ch. II, § 7. Proposition 6. Mumford, David; Oda, Tadao (2015). Algebraic Geometry II.