INITIAL SCHEMES OF VERY AFFINE SEVERI VARIETIES Contents ...

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INITIAL SCHEMES OF VERY AFFINE SEVERI VARIETIES JIHYEON JESSIE YANG Contents 1. Introduction 1 2. Preliminaries 2 3. Closed Subgroups of T∆ 6 4. Initial Schemes of Sev(∆, δ) 11 References 15 Abstract. Severi varieties are parameter spaces whose points correspond to nodal curves on toric surfaces. We study their initial schemes, which are certain flat degenerations. We find an explicit combinatorial description of them in terms of subdivisions of polygons.
  • linear order
  • tropical intersection theory
  • affine severi varieties
  • t∆
  • lattice point
  • classical severi variety
  • corresponding matrix m∂∆
  • dimension of the cone
  • constant term
  • dimension
Published : Wednesday, March 28, 2012
Reading/s : 24
Origin : stat.uiowa.edu
Number of pages: 4
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22S:130Instructor:Prof. R. RUSSO335-0817 205 SHrrusso@stat.uiowa.edu3:30-5 PMoffice hoursTues & FriOffice Hours:who seek out-of-class help from me are expected to have students excellent attendance in the lecture. Course Webpage:go tohttp://www.cs.uiowa.edu/~rrusso/then hitCOURSESText:Intro to Probability and Statistics for Engineers and Scientists rd  3ed., bySheldon M. Ross. Coverage= chapters 3, 4, 5 & parts of 6. You are expected to read the book. Format:Please do not arrive late or leave early.Class attendance is essential. Homework:Check the website on Thursday for theyou will work in teams of 5. assignment. HWis due in lecture, TWO Monday’s later.Each team makes a single submission. HWshould be neat & stapled, with names +section numbers in the top right corner. Late HW:< 5PM 2 days later= 50% penalty.< 5PM the next day = 25% penalty,Exams & Quizzes:In addition, Appx. ten 15-minute quizzes will be given (on Wednesday).a Midterm exam will be given during the semester, & a cumulative Final exam during Finals Week.Make-ups: Make-upexams/quizzes will be given on rare occasions.If something unexpected arises (emergency, illness, religious, etc.) let me know as soon as possible, and we will discuss your situationGrades: HOMEWORK10%  QUIZZES20-30% appx.10 quizzes - - most Wednesdays MIDTERMEXAM 20-30%in class, at the ½ way point CUMULATIVEFINAL EXAM30-40% duringFinals Week, as scheduled TOTAL100%As a rough guide"A" = 90%,"B" = 80%,"C" = 70%,"D" = 60%.Tutors:a Forlist of independent tutors go tohttp://www.stat.uiowa.edu/courses/tutors.htmlDisabled students:I would like to hear from anyone who has a disability which may require some modification of seating, testing, or other class requirements so that appropriate arrangements may be made. Please see me after class or during office hours. Policies:Course policies are governed by the College of Liberal Arts and Sciences. For University policies regarding Student Rights and Responsibilities go to http://www.clas.uiowa.edu/students/academic_handbook/"
DEO: Prof.Luke Tierney, 241 SH, 335-0712, luke-tierney@uiowa.eduJoint distributions Marginals: of Y: of X:  y  1  1  y= x  x  01y 0 Conditionals: of Xgiven Y = y of Ygiven X = x
y = x  1
Double expectation formula Varianceformula Bayes’ Theoremexamples 1) Suppose1% of a population uses an illegal drug.A drug test correctly  identifies95% of users, but produces a false positive for 2% of non-users.  FindP(user | +test). 2) 5red 1marble 2red 1marble  5whitewhite 8  BoxA BoxB A marble is transferred from A to B, then a marble is chosen from B. Find P( red from A| redfrom B) 3)Let θ denote the probability that a transplant patient survives at least 5 years. The table below gives the prior probabilities of five values ofθ basedon a poll of 10 surgeons. modellikelihood product priorposterior θ =decimals) (3 (2decimals)decimals) (2 .25 .10 .01 .001.01 .40 .10.04 .004.06 .50 .30.06 .018.26 .75 .30 .11.033 .47 .90 .20.07 .014.20 Four patients are tracked for 5 years, and the following table is constructed: patient 12 3 4 survival 5+5+ 3.85+
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