Syllabus/achievement requirements

Literature

Here are some relevant book chapters, articles, and links.

Hilbert schemes and Chow varieties

J. Kollár: Rational Curves of Algebraic Varieties, Springer 1996 (Chapter I)

D. Mumford: Lectures on curves on an algebraic surface, Princeton Univ. Press 1966.

R. Piene, M. Schlessinger: On the HIlbert scheme compactification of the space of twisted cubics. Amer. J. Math. 107:4 (1985), 761–774.

R. Piene: On the use of parameter and moduli spaces in curve counting.

Dawei Chen: Mori's program for the Kontsevich moduli space \overline{M_{0,0}}(P^3,3).

Y.-H. A. Lee: The Hilbert scheme of Curves in P^3. BA Thesis, Harvard 2000.

Algebraic spaces

M. Artin: Algebraic Spaces, Yale Univ. Press 1971

A. Knutson: Algebraic spaces, LNM Vol. 203, Springer 1071

Moduli spaces of curves

W. Fulton and R. Pandharipande: Notes on stable maps and quantum cohomology.

I. Coskun: Birational geometry of moduli spaces. Lecture notes, 2010

D. Edidin: Notes on the construction of the moduli space of curves. Recent Progress in Intersection Theory, Birkhauser 2000.

R. Pandharipande: Intersections of Q-divisors on Kontsevich's moduli space...

R. Vakil: The Moduli Space of Curves and Its Tautological Ring. Notices of the AMS 50(6), 647--658.

J. Kollar: Holomorphic and pseudo-holomorphic curves on rationally connected varieties.

Stacks

D. Edidin: What is... A Stack? Notices of the AMS 50(4), 458--459

B. Fantechi: Stacks for everybody. European Congress of Mathematics, Vol. I (Barcelona, 2000), 349--359, Progr. Math., 201, Birkh?user, Basel, 2001.

A guide to the literature on algebraic stacks

K. Behrend, B. Conrad, D. Edidin, W. Fulton, B. Fantechi, L. G?ttsche und A. Kresch: Algebraic stacks. In-progress book.

Published Apr. 9, 2010 9:52 AM - Last modified Feb. 27, 2023 11:26 AM