臺灣大學數學系演講博士生論文口試

演講者：林金毅
講  題：Del Pezzo 曲面之幾何
時  間：2014年1月27日 (星期一) 10:00
地  點：臺灣大學天數館305室
摘  要：
Given a singular del Pezzo surface X, i.e., a normal surface with at worst klt singularities and –KX nef and big, it is natural to ask the non-vanishing of anti-plurigenera h0(X,-mKX). In this paper, we consider surfaces with singularities of type  . There are two reasons for this. First of all, surfaces with singularities of type  has very nice combinatoric properties in the singular Riemann-Roch formula. We are able to derive an interesting type of nonvanishing.

Theorem. Suppose X is a del Pezzo surface with only singularities of the form  then h0(X,-mKX) for m=1 or 3.

Moreover, given a surface with cyclic quotient singularities, we develop a partial resolution via particular choices of weighted blowups called L-blowups, which transform cyclic quotient singularities to singularites of the form  . In principle, many of the leading Euler characteristics are preserved under L-blowups. However, situation varies depending on types of singularities. In any event, we have χ(X,-KX)= χ(Y,-KY) for any L-blowup Y→X such that Y has singularites of type  .