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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.
For a given genus g, the moduli space for curves C of genus g should contain a dense subset parameterizing those curves with the minimum in the way of special divisors. One goal of the theory is to 'count constants', for those curves: to predict the dimension of the space of special divisors (up to linear equivalence) of a given degree d, as a function of g, that must be present on a curve of ...
Download as PDF; Printable version; In other projects ... move to sidebar hide. In algebraic geometry, the Hurwitz scheme, is the scheme parametrizing pairs ...
The geometry of syzygies. A second course in commutative algebra and algebraic geometry. Graduate Texts in Mathematics. Vol. 229. New York: Springer-Verlag. xvi+243. ISBN 0-387-22215-4. Eisenbud, David; Harris, Joe (2016). 3264 and All That: A Second Course in Algebraic Geometry. Cambridge University Press. ISBN 978-1107602724.
The Bombieri–Lang conjecture is an analogue for surfaces of Faltings's theorem, which states that algebraic curves of genus greater than one only have finitely many rational points. [ 8 ] If true, the Bombieri–Lang conjecture would resolve the Erdős–Ulam problem , as it would imply that there do not exist dense subsets of the Euclidean ...
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]
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.
The ring of regular functions (that is the coordinate ring or more abstractly the ring of global sections of the structure sheaf) is a fundamental object in affine algebraic geometry. The only regular function on a projective variety is constant (this can be viewed as an algebraic analogue of Liouville's theorem in complex analysis).