Helix Structures in Quantum Cohomology of Fano Varieties
暫譯: Fano 多樣體的量子共形學中的螺旋結構

Cotti, Giordano, Dubrovin, Boris A., Guzzetti, Davide

Helix Structures in Quantum Cohomology of Fano Varieties
  • 出版商: Springer
  • 出版日期: 2024-10-29
  • 售價: $3,120
  • 貴賓價: 9.5 折 $2,964
  • 語言: 英文
  • 頁數: 236
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031690664
  • ISBN-13: 9783031690662
  • 相關分類: 量子 Quantum

    • 海外代購書籍(需單獨結帳)

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商品描述

This research monograph provides a comprehensive study of a conjecture initially proposed by the second author at the 1998 International Congress of Mathematicians (ICM). This conjecture asserts the equivalence, for a Fano variety, between the semisimplicity condition of its quantum cohomology and the existence of full exceptional collections in its derived category of coherent sheaves. Additionally, in its quantitative form, the conjecture specifies an explicit relation between the monodromy data of the quantum cohomology, characteristic classes, and exceptional collections. A refined version of the conjecture is introduced, with a particular focus on the central connection matrix, and a precise link is established between this refined conjecture and Γ-conjecture II, as proposed by S. Galkin, V. Golyshev, and H. Iritani. By performing explicit calculations of the monodromy data, the validity of the refined conjecture for all complex Grassmannians G(r, k) is demonstrated. Intended for students and researchers, the book serves as an introduction to quantum cohomology and its isomonodromic approach, along with its algebraic counterpart in the derived category of coherent sheaves.

商品描述(中文翻譯)

這本研究專著提供了一個全面的研究，針對第二作者在1998年國際數學家大會（ICM）上提出的猜想。這個猜想主張，對於Fano多樣體，其量子同調的半簡單性條件與其在相干層的導出類別中存在完整的例外集合是等價的。此外，在其定量形式中，該猜想明確指定了量子同調的單調數據、特徵類和例外集合之間的關係。引入了一個精煉版本的猜想，特別關注於中心連接矩陣，並建立了這個精煉猜想與S. Galkin、V. Golyshev和H. Iritani提出的Γ-猜想 II之間的精確聯繫。通過對單調數據進行明確計算，證明了該精煉猜想對所有複數Grassmannian G(r, k)的有效性。本書旨在為學生和研究人員提供量子同調及其等單調方法的介紹，以及其在相干層的導出類別中的代數對應。

作者簡介

Davide Guzzetti obtained his Ph.D. in Mathematical Physics in 2000 from the Scuola Internazionale Superiore di Studi Avanzati SISSA, Trieste, Italy. After holding research positions at RIMS, Kyoto University, Japan, and KIAS, Seoul, South Korea, he became a researcher at SISSA in 2011, and an associate professor in 2018.

Giordano Cotti obtained his Ph.D. in Geometry and Mathematical Physics from SISSA in 2017. He has held research positions at the Max Planck Institute for Mathematics in Bonn, Germany, and the University of Birmingham in the UK. Since 2020, he has been a researcher in the Group of Mathematical Physics at the University of Lisbon in Portugal.

Boris A. Dubrovin (1950-2019) obtained his Ph.D. in Geometry and Topology at Moscow State University under the supervision of S.P. Novikov. After obtaining his Habilitation in 1984, he was a full professor at Moscow State University (1988-1993) and at SISSA from 1993 to 2019.

作者簡介(中文翻譯)

達維德·古澤提於2000年在義大利的國際高等研究院(SISSA)獲得數學物理學博士學位。在日本京都大學的RIMS和南韓首爾的KIAS擔任研究職位後，他於2011年成為SISSA的研究員，並於2018年晉升為副教授。

喬丹諾·科提於2017年在SISSA獲得幾何學和數學物理學博士學位。他曾在德國波恩的馬克斯·普朗克數學研究所和英國伯明翰大學擔任研究職位。自2020年以來，他一直是葡萄牙里斯本大學數學物理組的研究員。

鮑里斯·A·杜布羅文（1950-2019）在莫斯科國立大學獲得幾何學和拓撲學博士學位，指導教授為S.P.諾維科夫。1984年獲得Habilitation後，他於1988年至1993年在莫斯科國立大學擔任正教授，並於1993年至2019年在SISSA任教。

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