UC Riverside Algebraic Geometry Seminar

Date	Speaker	Title	Abstract
Tuesday, October 04, 2016 Start: 2:10 PM Location: Surge 282 (*)	Ziv Ran UC Riverside	Filling Groovy: Generic Projections	We consider a general fibre of given length in a generic projection of a variety. Under the assumption that the fibre is of local embedding dimension 2 or less, an assumption which can be checked in many cases, we prove that the fibre is reduced and its image on the projected variety is an ordinary multiple point.
Tuesday, October 11, 2016 Start: 2:10 PM Location: Surge 268	Daniel Chun UC Riverside	Non-vanishing of syzygies and secant constructions, Part I	After an introduction into the world of syzygies, we consider various techniques to explicity compute syzygies of projective varieties of large degree. Although we will look at some vanishing results, our focus will primarily be on proving non-vanishing of syzygies through an induction involving secant constructions, which is an approach developed by Lazarsfeld and Ein in their paper "Asymptotic syzygies of algebraic varieties."
Tuesday, October 18, 2016 Start: 2:10 PM Location: Surge 268	Daniel Chun UC Riverside	Non-vanishing of syzygies and secant constructions, Part II	After an introduction into the world of syzygies, we consider various techniques to explicity compute syzygies of projective varieties of large degree. Although we will look at some vanishing results, our focus will primarily be on proving non-vanishing of syzygies through an induction involving secant constructions, which is an approach developed by Lazarsfeld and Ein in their paper "Asymptotic syzygies of algebraic varieties."
Tuesday, October 25, 2016 Start: 2:10 PM Location: Surge 268	Daniel Chun UC Riverside	Non-vanishing of syzygies and secant constructions, Part III	After an introduction into the world of syzygies, we consider various techniques to explicity compute syzygies of projective varieties of large degree. Although we will look at some vanishing results, our focus will primarily be on proving non-vanishing of syzygies through an induction involving secant constructions, which is an approach developed by Lazarsfeld and Ein in their paper "Asymptotic syzygies of algebraic varieties."
Tuesday, November 01, 2016 Start: 2:10 PM Location: Surge 268	Hwayoung Lee Visiting UC Riverside	Mirror symmetry on complete intersection K3 surfaces	This talk is based on joint work with Kenji Hashimoto and Kazushi Ueda. On complete intersection K3 surfaces in Weighted projective 4-fold, we show that the duality by (an analogue of) transposition mirror construction of Berglund-Huebsch is equal to Dolgachev's mirror symmetry.
Tuesday, November 08, 2016 Start: 2:10 PM Location: Surge 268	Humberto Diaz UC Riverside	Algebraic Cycles mod n	In this talk, I will give an overview of the group of algebraic cycles on a smooth projective variety and some infinitude results for this group. I will also report on work in progress for a new case of infinitude with mod n coefficients.
Tuesday, November 15, 2016 Start: 2:10 PM Location: Surge 268	Youngsu Kim UC Riverside	Castelnuovo-Mumford Regularity; a counter example of McCullough and Peeva	Castelnuovo-Mumford regularity is an invariant of a graded-module over a polynomial ring, which controls the maximum shifts of the graded syzygies. There has been a long standing conjecture by Eisenbud-Goto. Roughly speaking, it says that the regularity of a graded ideal is bounded by its multiplicity (or degree). There have been several positive results in both commutative algebra and algebraic geometry. Recently, Jason McCullough and Irena Peeva announced a counter-example to the regularity conjecture. In this talk, we briefly review the history of the conjecture and the construction of their example.
Tuesday, November 22, 2016 Start: 2:10 PM Location: Surge 268	Stefano Vidussi UC Riverside	The slope of surfaces of Albanese dimension one	The geography of minimal surfaces of general type is constrained by the Bogomolov-Miyaoka-Yau line and the Noether line. Sommese [84] proved that the set of attainable slopes is dense in the region determined by these lines. In this talk we will discuss how such result can be recast using only surfaces of Albanese dimension one.
Tuesday, November 29, 2016 Start: 2:10 PM Location: Surge 268	Jose Gonzalez UC Riverside	Some non-finitely generated Cox rings	Cox rings generalize the homogenous coordinate rings of toric varieties. The main problem in the theory of Cox rings is to determine whether they are finitely generated. We overview some non-finite generation results for the Cox rings of weighted projective planes blown up at a point, which extend work of Goto, Nishida and Watanabe. These results have been used by several authors to study the Cox rings of the moduli space of pointed genus zero curves.