![]() ![]() The goal is to compute the defining equations of the special fiber ring and the Rees ring of these ideals. For each fixed $d$ these ideals are all equivalent, up to change of coordinates. Let $I$ be a Gorenstein ideal generated by all the generators of $m^2$ except for one. Let $m =(x_1, \ldots, x_d)$ be the maximal homogenous ideal of $R$. Let $R=k$ be a polynomial ring in $d$ variables over a field $k$. 26, 2018 Speaker Whitney Liske (Notre Dame) Title Defining equations of the Rees algebra for a family of ideals Abstract This is joint work in progress with Johan de Jong. In particular, I will sketch a totally canonical definition of the functor Rf_! in etale cohomology. In this talk I'll define an analogous compactification in the setting of schemes, explain its basic properties, and give some applications. ![]() The one-point compactification of a locally compact Hausdorff space is a classical and useful construction. 19, 2018 Speaker David Hansen (Notre Dame) Title The one-point compactification of a scheme Abstract We will discuss some finiteness properties of difference algebraic groups and applications to differential equations. The theory of these groups has some similarities with the theory of linear algebraic groups. 12, 2018 Speaker Michael Wibmer (Notre Dame) Title Difference algebraic groups Abstractĭifference algebraic groups are subgroups of the general linear group defined by algebraic difference equations in the matrix entries. Our technique is substantially simpler than previous approaches to this question, and has already led to improved bounds for the Kobayashi Conjecture. ![]() We prove that (a slightly strengthened version of) the Green-Griffiths-Lang Conjecture in dimension 2n implies the Kobayashi Conjecture in dimension n. We discuss two well-known conjectures on entire curves on very general high-degree hypersurfaces X in P^n: the Green-Griffiths-Lang Conjecture, which says that the entire curves lie in a proper subvariety of X, and the Kobayashi Conjecture, which says that X contains no entire curves. 5, 2018 Speaker Eric Riedl (Notre Dame) Title A Grassmannian technique and the Kobayashi Conjecture AbstractĪn entire curve on a complex variety is a holomorphic map from the complex numbers to the variety. ![]() This is a joint work with Giulio Caviglia. In this talk we discuss the existence of sharp upper bounds for the syzygies of I in terms of the degrees of the regular sequence f and of the Hilbert function or the Hilbert polynomial of I. Let S be a polynomial ring over a field and I a homogeneous ideal containing a regular sequence f = f_1. 29, 2018 Speaker Alessio Sammartano (Notre Dame) Title Upper bounds for Betti numbers in Hilbert schemes of complete intersections Abstract The Hilbert scheme of a pair of linear spacesĪug. MMP and wall-crossing for Bridgeland moduli spaces on Enriques and bielliptic surfacesīrill-Noether Theorems for sheaves on surfaces The Witten zeta function of projective varieties Hypergraph encodings of arbitrary toric ideals Marius Vlădoiu (University of Bucharest / Purdue) Symbolic and Ordinary Powers of Ideals in Hibi Rings Group realization and embedding problems in differential Galois theory The one-point compactification of a schemeĭefining equations of the Rees algebra for a family of idealsĭavid Harbater (University of Pennsylvania) Upper bounds for Betti numbers in Hilbert schemes of complete intersectionsĪ Grassmannian technique and the Kobayashi Conjecture Twisted generalized Weyl algebras over polynomial ringsįujita type conjectures for pushforwards of pluricanonical sheaves Syzygies of Determinantal Thickenings via General Linear Lie Superalgebra Representationsĭaniele Rosso (Indiana University Northwest) Open subgroups of p-adic algebraic groupsĪn example of liftings with different Hodge numbersĪn analogue of the Hartshorne-Polini theorem in positive characteristicĭuality, finiteness, and cohomology jump loci The seminar will meet on Wednesdays, 3:00–4:00pm in 258 Hurley unless otherwise noted. To volunteer to give a talk, or for anything else regarding the seminar, contact Claudiu Raicu. Algebraic Geometry/Commutative Algebra Seminar, Department of Mathematics, University of Notre Dame, 2018-2019 Algebraic Geometry/Commutative Algebra Seminar, 2018–2019 ![]()
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