University of Utah
Algebraic Geometry Seminar
Spring 2008: Tuesdays 3:30-4:30, LCB 323

Schedule of upcoming talks:

Click on the title of a talk for the abstract (if available).

Date Speaker Title
January 9, LCB 215
Andrew Snowden
(Princeton University)
The equations of the GIT quotient (P1)n/PGL(2) Let n >= 4 be an even integer and let Mn be the moduli space of n points on P1 modulo the action of PGL(2), thought of as the GIT quotient (P1)n/PGL(2). The space Mn has a natural projective embedding; let Rn be its projective coordinate ring. The ring Rn was studied classically in the context of invariant theory. In the late nineteenth centruy, Kempe proved that Rn is generated by its degree one piece. Since that time however, generators for the ideal of relations have not been determined. I will talk about my recent work with Howard, Millson and Vakil towards understanding generators of this ideal. Two of our results: 1) the ideal of relations is always generated in degrees <= 3; and 2) for all n not equal to 6 the image of Mn in projective space is cut out by quadrics.
January 15
3 pm, LCB 225
Dave Anderson
(University of Michigan)
Chern class formulas for G2 degeneracy loci Let V be a vector bundle of rank n on a variety X, with subbundles E and F of respective ranks e and f. The locus of points of X where the fibers of E and F intersect in dimension more than e+f-n is a basic example of a degeneracy locus, and it is useful to have formulas for the cohomology classes of such loci in terms of the Chern classes of E, F, and V. Many variations are possible: there should be one for each Lie type, and for each element of the corresponding Weyl group. For classical types, formulas were given by Giambelli-Thom-Porteous, Kempf-Laksov, Harris-Tu, and Fulton. In this talk, I will give formulas corresponding to exceptional type G2. Along the way, I'll discuss octonion bundles, and describe the G2 flag variety in concrete, linear-algebraic terms.
January 22 Tommaso de Fernex A vanishing theorem for log canonical pairs
January 29
Fumitoshi Sato
The orbifold cohomology of abelian and non-abelian quotients Let G be a semisimple Lie group and which is acting on X. Then we consider X//G and X//T where T is a maximal torus of G. We will explain a comparison theory of orbifold cohomologies of X//G and X//T when both spaces are orbifolds.
January 31, 2.45 pm
(LCB 323)
Sam Payne
(Clay Institute/Stanford)
Frobenius splitting of toric varieties
See also: February 1
Comm. Algebra seminar
Mihnea Popa (UIC)
February 5
Tyler Jarvis
The Witten equation, mirror symmetry and quantum singularity theory I will describe recent joint work with Huijun Fan and Yongbin Ruan in which we construct, for every non-degenerate quasi-homogeneous singularity, a moduli space of decorated stable curves and a virtual cycle on that space. In the special case of the Ar-1 singularity, our constructions give a refinement of the theory of r-spin curves. For simple singularities the resulting Frobenius algebra is "mirror dual" to the Milnor ring of the singularity. For other singularities, we conjecture a more complicated mirror symmetry relation. Finally, I will describe some work in progress, in which we generalize the Faber-Shadrin-Zvonkine proof of the Witten conjecture for r-spin curves (An) to prove an analogous theorem about integral hierarchies associated to the simple singularities D2n and E6, E7 and E8
See also: February 8
Comm. Algebra seminar
Fumitoshi Sato (KIAS)
February 12
Mircea Mustaţă
(University of Michigan)
Towards an inductive approach to singularities of pairs
See also: February 14
Departmental Colloquium
Mircea Mustaţă
(University of Michigan)
See also: February 15, 4pm
Representation Theory Seminar
Pramod Achar
(Louisiana State)
February 19
3 pm, LCB 222
Matthew Ballard
(University of Washington)
Graded reconstruction for Gorenstein varieties Singularity of a projective variety manifests itself categorically in the loss of essential surjectivity of the natural inclusion of the perfect derived category into the bounded derived category of coherent sheaves. We shall see, that when working over a perfect field, these two categories determine each other through a type of duality. Using this knowledge, we can then extend Bondal and Orlov's result on reconstruction of a smooth projective variety from the graded structure on the bounded derived category of coherent sheaves to the case of Gorenstein projective varieties.
February 26 Milena Hering (IMA) The moduli space of points in P1 and the Koszul property
March 4 Christopher Hacon Deformation of canonical pairs
March 11 Gueorgui Todorov The Gromov-Witten potential of the local P(1,2)
March 18
No Seminar
(Spring break)
March 25
Emanuele Macri
(University of Bonn, Germany)
Derived equivalences of K3 surfaces and orientation We will consider the problem of describing equivalences between the derived categories of coherent sheaves of smooth projective K3 surfaces. After recalling the `classical' Derived Torelli Theorem, we will prove a conjecture by Szendroi which improves the result and involves the preservation of the orientation of some 4-dimensional space in the real cohomology of the K3 surfaces. Our approach relies on the proof of the same conjecture for generic (non-projective) K3 surfaces. This is joint work with D. Huybrechts and P. Stellari (arXiv:0710.1645).
April 1
Alfred Chen
(National Taiwan University/Utah)
Some further remarks on birational geometry of threefolds We notice that our previous study on the basket of singularities also applicable to weak Q-Fano threefolds. More precisely, we obtained the following results: 1. non-vanishing of antiplurigenera 2. lower bound for anti-canonical volume for weak Q-Fano threefolds. This bound is sharp.

We will also describe the relation between flips and "unpacking", which provide another viewpoint to see the termination of flips.

April 8 Tommaso de Fernex Deformation of canonical pairs, part 2
April 15
Charles Cadman
Relating relative and orbifold Gromov-Witten invariants
April 22 ??? TBA

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This web page is maintained by Arend Bayer; it was shamelessly copied from Izzet Coskun's page, which in turn was shamelessly copied from Ravi Vakil's page, which in turn was shamelessly copied from Pasha Belorousski's page at the University of Michigan.