Semestr Zimowy 2018/2019

Seminarium odbywa się we wtorki w sali 118 w godzinach 10:15 — 11:45

 

 

TERMIN	WYKŁADOWCA	TEMAT
9 października 2018	Krishna Hanumanthu (Chennai, India)	Some results on Seshadri constants (Abstrakt)
23 października 2018	Janusz Gwoździewicz	Owale na plaszczyznach skończonych
30 października 2018	Grzegorz Malara	Resolutions II
6 listopada 2018	working group	discussion of a proof in Arrondo’s script
20 listopada 2018	Halszka Tutaj-Gasińska	Lincoln, a short report
27 listopada 2018	Lanckorona workshop	Symbolic defect
4 grudnia 2018	Tomasz Szemberg	Ruled varieties
18 grudnia 2018	Piotr Pokora	@Hot topic
15 stycznia 2019	bez seminarium	spotkanie na UJ
22 stycznia 2019	bez seminarium	wyjazdy Loughborough, Freiburg
29 stycznia 2019	Evelia R. Garcia Barroso	Gaps of semigroups associated with singular plane branches (Abstrakt)

 

• Abstract of Prof. Hanumanthu talk:
  Let X be a projective variety and let L be an ample line bundle on X. For a point x in X, the Seshadri constant of L is defined to be the infimum of ratios L.C/m, where the infimum is taken over all curves C passing through the point x and m denotes the multiplicity of C at x. These constants arose out of an ampleness criterion of Seshadri and were defined by Demailly in 1990. They turned out to be very important to the study of local positivity of line bundles on projective varieties and are now the focus of a lot of research in algebraic geometry. In this talk we will discuss two recent results on Seshadri constants. The first result (joint work with B. Harbourne) considers blow ups X of the projective plane at 9 or more general points. Assuming a conjecture related to the so-called SHGH Conjecture, we prove that Seshadri constants for suitably constructed ample line bundles on X are irrational numbers. In the second result (joint work with I. Biswas, D. S. Nagaraj and P. Newstead), we consider Grassmannian bundles associated to a vector bundle E on an arbitrary smooth curve. Under some conditions on the Harder-Narasimhan filtration of E, we prove some results on Seshadri constants for ample line bundles on the Grassmannian bundles associated to E.

• Abstract of Prof. Barroso talk:
  A branch is a curve C = [f = 0], where f in C[[x; y]] is irreducible. We associate with C a numerical semigroup, that is a subset S of natural numbers, which contains zero, is closed with respect to addition and N without S is finite. The elements of the complement of S are called gaps of S. Gaps play an important rol on the analytic classification of plane branches. In this talk we will describe the set of gaps of S. This is a joint work with J. I. García García, M.A. Moreno Frías and A. Vigneron Tenorio.