Titlebook: An Invitation to Modern Enumerative Geometry; Andrea T. Ricolfi Book 2022 The Editor(s) (if applicable) and The Author(s), under exclusive

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persistence

Background Material,o sketch the algebraic definition of Chern classes, and conclude the chapter with a brief overview on representable functors, that will be needed to define fine moduli spaces and universal families. By . we will always mean an algebraically closed field. Most of the time in later chapters, we will s

責(zé)難

小丑

,The Atiyah–Bott Localisation Formula, Vainsencher (Mat Contemp 20:1–70, 2001) and Anderson (Introduction to equivariant cohomology in algebraic geometry. Contributions to algebraic geometry, European Mathematical Society, Zürich, EMS Series of Congress Reports, 2012). 16th School of Algebra, Part I (Brasília, 2000). We note that the re

hallow

Applications of the Localisation Formula, Contemp 20:1–70, 2001) was of great inspiration for the first three sections in this chapter, and we take the opportunity to refer the reader to loc. cit. for more examples of application of the localisation formula (upgraded to equivariant Chow theory) in enumerative geometry.

雪崩

The Toy Model for the Virtual Class and Its Localisation,from (see Remark 10.1.15). This construction has historically two approaches: that of Li–Tian (J Am Math Soc 11(1):119–174, 1998) and that of Behrend–Fantechi (Invent Math 128(1):45–88, 1997). In this chapter we shall explicitly construct the perfect obstruction theory on a scheme of the form .?=?.(

向前變橢圓

,DT/PT Correspondence and a Glimpse of Gromov–Witten Theory, and Pandharipande–Thomas invariants. This relation (Theorem 12.1.1) was proved by Bridgeland (J Am Math Soc 24(4):969–998, 2011) and Toda (J Am Math Soc 23(4):1119–1157, 2010). The classical setup, summarised in the next section, involves a . Calabi–Yau 3-fold. In Sect. 12.2 we will exploit virtual

curriculum

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