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Harris is well known for several of his books on algebraic geometry, notable for their informal presentations: Principles of Algebraic GeometryISBN 978-0-471-05059-9, with Phillip Griffiths [2] Geometry of Algebraic Curves, Vol. 1 ISBN 978-0-387-90997-4, with Enrico Arbarello, Maurizio Cornalba, and Phillip Griffiths; William Fulton, Joe Harris.
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He has published on algebraic geometry, differential geometry, geometric function theory, and the geometry of partial differential equations. Griffiths serves as the Chair of the Science Initiative Group. [2] He is co-author, with Joe Harris, of Principles of Algebraic Geometry, a well-regarded textbook on complex algebraic geometry. [3]
In algebraic geometry, the Grassmann d-plane bundle of a vector bundle E on an algebraic scheme X is a scheme over ... Eisenbud, David; Joe, Harris (2016), 3264 and ...
Enrico Arbarello, Maurizio Cornalba, Phillip Griffiths, Joe Harris. Geometry of algebraic curves. vol 1 Springer, ISBN 0-387-90997-4, appendix A. Phillip Griffiths and Joe Harris, Principles of algebraic geometry, Wiley, ISBN 0-471-05059-8, chapter 2, section 1. Robin Hartshorne (1977): Algebraic geometry, Springer, ISBN 0-387-90244-9.
Eisenbud, David; Harris, Joe (2016), 3264 and All That: A Second Course in Algebraic Geometry, Cambridge University Press, ISBN 978-1107602724; Kleiman, Steven L. (1974), "The transversality of a general translate", Compositio Mathematica, 28: 287– 297, MR 0360616
Abelian differentials usually mean differential one-forms on an algebraic curve or Riemann surface. Quadratic differentials (which behave like "squares" of abelian differentials) are also important in the theory of Riemann surfaces. Kähler differentials provide a general notion of differential in algebraic geometry.
Harris, Joe (1995), Algebraic Geometry: A First Course, Berlin, New York: Springer-Verlag, ISBN 978-0-387-97716-4 Hassett, Brendan (2007), Introduction to Algebraic Geometry , Cambridge: Cambridge University Press, p. 154, doi : 10.1017/CBO9780511755224 , ISBN 978-0-521-69141-3 , MR 2324354