Reading seminar in algebraic geometry.
Fall 2017. Surface singularities

This semester the reading seminar will study surface singularities in algebraic geometry, including resolutions and deformations.

The seminar will consist of introductory talks by faculty followed by talks by graduate students. We will attempt to make the seminar accessible to everyone.

The seminar will meet on Monday afternoons, 3:00--4:00PM in LGRT 1114.




Tentative Schedule

9/8. Organizational meeting, 4:30PM, LGRT 1634.

9/18. Paul Hacking. Surface singularities: Resolutions [R], [M61], [R97]

9/25. Jenia Tevelev. Surface singularities: Deformations [A76], [I12]

10/2. Jenia Tevelev. Flatness in terms of syzygies [A76]

10/9. No seminar (Columbus day).

10/16. Eduardo Cattani. Degenerations of algebraic varieties and Hodge theory. [G84]

10/23. Luca Schaffler. Q-Gorenstein deformations of surface singularities. [KSB88]

10/30. Arie Stern Gonzalez. Q-Gorenstein deformations of surface singularities. II. [KSB88]

11/6. Sebastian Torres. Topology of normal singularities on surfaces. [M61]

11/13. Angelica Simonetti. Cusp singularities of complex surfaces. [L81], [GHK15]

11/20. No seminar (Thanksgiving).

11/27. Jennifer Li. ADE singularities. [R], [D79]

12/4. Yu Fu. Bounds on singularities of stable surfaces. [RU]

12/11. Max Hully. Resolution of singularities for surfaces (in characteristic zero) -- Zariski's proof. [L75], [K07].




References

[A76] M. Artin, Lectures on deformations of singularities, Lectures on Mathematics 54, Tata Institute of Fundamental Research, 1976. TIFR

[D79] A. Durfee, Fifteen characterizations of rational double points and simple critical points, Enseign. Math. (2) 25 (1979), no. 1--2, 131--163.

[G84] Topics in transcendental algebraic geometry. Edited by Phillip Griffiths. Ann. of Math. Stud. 106, P.U.P., 1984.

[GHK15] M. Gross, P. Hacking, and S. Keel, Mirror symmetry for log Calabi-Yau surfaces I, Publ. Math. Inst. Hautes Études Sci. 122 (2015), 65--168.

[I12] N. Ilten, Versal deformations and local Hilbert schemes, J. Softw. Algebra Geom. 4 (2012), 12--16. arxiv.

[K07] J. Kollár, Lectures on resolution of singularities, Ann. of Math. Stud. 166, P.U.P, 2007. googlebooks.

[KM98] J. Kollár and S. Mori, Birational geometry of algebraic varieties, C.U.P 1998, Chapter 4. googlebooks.

[KSB88] J. Kollár and N. Shepherd-Barron, Threefolds and deformations of surface singularities, Invent. Math. 91 (1988), no. 2, 299--338.

[L75] J. Lipman, Introduction to resolution of singularities, Algebraic geometry (Proc. Sympos. Pure Math., Vol. 29, Arcata, 1974), 187--230, A.M.S., 1975.

[L81] E. Looijenga, Rational surfaces with an anticanonical cycle, Ann. of Math. (2) 114 (1981), no. 2, 267--322.

[M61] D. Mumford, The topology of normal singularities of an algebraic surface and a criterion for simplicity, Inst. Hautes &‚ÄĆEacute;tudes Sci. Publ. Math. No. 9 (1961), 5--22. NUMDAM.

[RU] J. Rana and G. Urzúa, Optimal bounds for T-singularities in stable surfaces, preprint arXiv:1708.02278v1 [math.AG]. arXiv.

[R] M. Reid, Du Val singularities, manuscript. pdf.

[R97] M. Reid, Chapters on algebraic surfaces in Complex algebraic geometry (Park City, UT, 1993), 3--159, IAS/Park City Math. Ser. 3, A.M.S., 1997, Chapter 4. arxiv.




Links to the seminar from previous semesters.

Birational geometry, Spring 2016.
Algebraic surfaces, Fall 2016.
Fano varieties, Fall 2015
The Hitchin system, character varieties, and related topics, Spring 2015
Holomorphic symplectic varieties and Hyperkahler manifolds, Fall 2014
Syzygies, Spring 2014
Toric varieties, Fall 2013
Derived categories in algebraic geometry, Spring 2013
Deformation theory, Fall 2012
Curves, K3 surfaces, and Fano 3-folds, Spring 2012
Topics in algebraic geometry, Fall 2011
Surfaces of general type, Spring 2011
Algebraic surfaces, Fall 2010.
Stability conditions on derived categories and wall crossing, Spring 2010
Mirror symmetry and tropical geometry, Fall 2009
Deformation theory, Fall 2008
Green's Conjectures, Spring 2008
Bridgeland Stability, Fall 2007.
Minimal Model Program, Spring 2007
Commutative Algebra and Polyhedra Seminar, Spring 2006.
Geometry and Algebra of Polyhedra Seminar, Fall 2005.
Commutative Algebra Seminar, 2004-2005



This page is maintained by Paul Hacking hacking@math.umass.edu