Theta-characteristics on algebraic curves

Author:
Joe Harris

Journal:
Trans. Amer. Math. Soc. **271** (1982), 611-638

MSC:
Primary 14H99; Secondary 14C20, 14K25

MathSciNet review:
654853

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Abstract: The theory of theta-characteristics is developed algebraically, so that it may be applied to possibly singular and/or reducible algebraic curves. The configuration of theta-characteristics on a curve is described in terms of its singularities, with applications to the geometry of plane quartic curves and the problem of Appolonius. Some results on Gorenstein local rings are appended.

**[1]**H. F. Baker,*Principles of geometry*, Vol. IV, Chapter II; Cambridge Univ. Press, 1925.**[2]**E. Griffin, Thesis, Harvard Univ., Cambridge, Mass., 1982.**[3]**Phillip Griffiths and Joseph Harris,*Principles of algebraic geometry*, Wiley-Interscience [John Wiley & Sons], New York, 1978. Pure and Applied Mathematics. MR**507725****[4]**H. Hilton,*Plane algebraic curves*, Oxford, 1920.**[5]**Joe Harris,*Galois groups of enumerative problems*, Duke Math. J.**46**(1979), no. 4, 685–724. MR**552521****[6]**Heisuke Hironaka,*On the arithmetic genera and the effective genera of algebraic curves*, Mem. Coll. Sci. Univ. Kyoto. Ser. A. Math.**30**(1957), 177–195. MR**0090850****[7]**Serge Lang,*On quasi algebraic closure*, Ann. of Math. (2)**55**(1952), 373–390. MR**0046388****[8 D]**David Mumford,*Theta characteristics of an algebraic curve*, Ann. Sci. École Norm. Sup. (4)**4**(1971), 181–192. MR**0292836****[9]**G. Salmon,*Conic sections*, Longman, Greens & Co., London, 1879.**[10]**-,*Higher plane curves*, Hodges, Foster & Co., Dublin, 1879.**[11]**C. T. C. Wall,*Nets of quadrics, and theta-characteristics of singular curves*, Philos. Trans. Roy. Soc. London Ser. A**289**(1978), no. 1357, 229–269. MR**0506258**

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1982-0654853-6

Article copyright:
© Copyright 1982
American Mathematical Society