Semestr Zimowy 2019/2020

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

 

TERMIN	WYKŁADOWCA	TEMAT
8 października 2019	Evelia Rosa  García Barroso (La Laguna)	Contact exponent and the Milnor number of plane curve singularities (Abstrakt)
22 października 2019	Justyna Szpond	Hiperpowierzchnie i osobliwości
29 października 2019	Halszka Tutaj-Gasińska	Obwiednie algebraiczne i polarność
5 listopada 2019	Grzegorz Malara	Hiperpowierzchnie stopnia 2 i polarność
26 listopada 2019	Tomasz Szemberg	Hiperpowierzchnie w $P^2$ i $P^3$
3 grudnia 2019	Iman Bahmani Jafarloo	On the containment problem for fat points (Abstrakt)
17 grudnia 2019	Marcin Dumnicki	Systemy liniowe I
14 stycznia 2020	Marcin Dumnicki	Systemy liniowe II
21 stycznia 2020	Janusz Gwoździewicz	Przekształcenia Cremony I
28 stycznia 2020	Janusz Gwoździewicz	Przekształcenia Cremony II

 

• Abstract of Prof. Barroso talk:
  We investigate properties of the contact exponent (in the sense of Hironaka) of plane algebroid curve singularities over algebraically closed fields of arbitrary characteristic. We prove that the contact exponent is an equisingularity invariant and give a new proof of the stability of the maximal contact. Then we prove a bound for the Milnor number and determine the equisingularity class of algebroid curves for which this bound is attained. We do not use the method of Newton’s diagrams. Our tool is the logarithmic distance developed in [Garcia Barroso, E. and A. Ploski. An approach to plane algebroid branches. Rev. Mat. Complut., 28 (1) (2015), 227-252.]. This is a joint work with Arkadiusz Płoski.
• Abstract of Iman Jafarloo talk:
  Given an ideal I, the containment problem is concerned about finding the values m and r such that the m-th symbolic power of I is contained in its r-th ordinary power. In order to study this problem, it is useful, given an ideal I, to introduce an asymptotic quantity, known as resurgence and denoted by $r(I)$, defined as $r(I)=sup\{m/r: I^(m)$ is not contained in $I^r\}$. In this talk I consider the containment problem focusing on the ideals of fat points and I show how to compute the resurgence for two particular classes of sub-schemes. Specifically, we study the fat points sub-schemes whose supports are n collinear points and any three distinct points in $P^N$ for all $N\geq 2$.