Autorentext

Ivan Cheltsov is Professor at the University of Edinburgh, and his research interests include birational geometry and K-stability of Fano varieties. He is author of 3 books and 126 papers written together with 52 co-authors. Ivan has organized research meetings in Auckland, Beijing, Cambridge, Durham, Edinburgh, Fuerteventura, Istanbul, Levico Terme, London, Magadan, Melbourne, Moscow, New York, Oberwolfach, Pipa, Pohang, Easter Island, Shanghai, Sochi, Spitsbergen, Stony Brook, Sydney, Tianjin, Wakkanai, Vladivostok. Since 1995, Ivan is married to Elena Cheltsova: they have three children (Ivan, Fedor, Ekaterina) and cat Kuzya. Aside of Mathematics, Ivan enjoys traveling, reading and cycling his Brompton bicycle. Jesus Martinez-Garcia is Senior Lecturer in Pure Mathematics at the University of Essex (UK). He obtained his PhD at the University of Edinburgh in 2013 and has held research positions at the University of Bath (UK), Johns Hopkins University (US) and the Max Planck Institute for Mathematics (Germany). His research is in algebraic geometry with special emphasis on birational geometry, moduli spaces, K-stability, Fano varieties and computational algebraic geometry. Martinez-Garcia has written one book, several research articles and two software packages and he has co-organised more than 10 research meetings, including the annual international conference AGGITatE as well as several research seminars.

Klappentext

ZAG Handbook of Algebraic Geometry provides an expansive collection of extended summaries of all the research talks given at the worldwide ZAG (Zoom Algebraic Geometry) Seminar as well as contributed short notes.

Inhalt

Table of Contents

1. Algebraic geometry in the times of Covid
   Ivan Cheltsov and Jesus Martinez-Garcia

2. Models of Fano 3-folds
   Hamid Abban

3. Weighted Ehrhart polynomials and series for the standard simplex
   Praise Adeyemo

4. Advances in moduli theory
   Jarod Alper

5. Normal form of a holomorphic Lagrangian submanifold
   Ekaterina Amerik

6. Koszul modules and applications
   Marian Aprodu

7. Euler characteristics of aspherical Kähler manifolds
   Donu Arapura

8. Birational geometry of Calabi-Yau pairs and Cremona transformations
   Carolina Araujo

9. Enumerating punctured log maps via wall-crossing
   Hulya Arguz

10. Biregular and birational geometry of rational nodal quartic double solids
    Artem Avilov

11. Chern character of quantizable sheaves
    Vladimir Baranovsky and Victor Ginzburg

12. Vector bundles on Fano threefolds and K3 surfaces
    Arnaud Beauville

13. Cylinders in Del Pezzo surfaces with Du Val singularities
    Grigory Belousov

14. Approximation of differentiable submanifolds by real algebraic subvarieties
    Olivier Benoist

15. Kähler-Einstein metrics, Archimedean zeta functions and phase transitions
    Robert Berman

16. Geometry of 3-dimensional Del Pezzo fibrations in positive characteristic
    Fabio Bernasconi

17. Geometry of polarised varieties
    Caucher Birkar

18. On properness of K-moduli spaces and optimal destabilizations
    Harold Blum

19. Surface with ample canonical bundle and Kuranishi space a nonreduced point
    Christian Boehning

20. Projective geometry approach to the Jacobian conjecture
    Alexander Borisov

21. Explicit equations of surfaces of general type
    Lev Borisov

22. General type results for moduli of hyperkähler varieties
    Emma Brakkee

23. Geometric structures on spaces of quadratic differentials
    Tom Bridgeland

24. Extending Tom and Jerry for Fano 3-folds
    Gavin Brown, Stephen Coughlan and Tom Ducat

25. Supercycles and stable supermaps
    Ugo Bruzzo and Daniel Hernandez Ruiperez

26. Arcs and singularities
    Nero Budur

27. Chern-Weil theory and Hilbert-Samuel theorem for semipositive singular toroidal metrics
    Jose Ignacio Burgos Gil

28. Index 2 Fano 3-folds and double covers
    Livia Campo

29. Uniqueness of enhancements of triangulated categories
    Alberto Canonaco, Amnon Neeman and Paolo Stellari

30. On the birational geometry of foliations
    Paolo Cascini

31. Effective cones of moduli spaces of stable rational curves and blown up toric surfaces Ana-Maria Castravet

32. Nodal surfaces, coding theory, and cubic discriminants
    Fabrizio Catanese

33. The minimal model program for arithmetic surfaces enriched by a Brauer class
    Daniel Chan

34. Low dimensional components in the K-moduli of smoothable Fano 3-folds
    Ivan Cheltsov

35. Remarks on n-folds of type (1,n)
    Jungkai Chen

36. Singularities on toric fibrations
    Yifei Chen and Caucher Birkar

37. On the distribution of canonical volumes and moduli spaces of varieties of general type
    Meng Chen

38. Subadditivity theorem for Okounkov bodies
    Sung Rak Choi

39. Enumeration of Terracini schemes
    Ciro Ciliberto

40. Numerical characterization of complex torus quotients
    Benoit Claudon

41. Slope inequalities and ample cone of KSB moduli spaces
    Giulio Codogni

42. The cohomology of the moduli space of sheaves on surfaces
    Izzet Coskun

43. Orbifold quot schemes via the le Bruyn-Procesi theorem
    Alastair Craw

44. On quadratic points on intersections of two quadrics
    Brendan Creutz and Bianca Viray

45. Deformations of exterior differential ideals and applications
    Fernando Cukierman

46. Log minimal model program for Kähler 3-folds
    Omprokash Das

47. CSCK metrics on rank one spherical Fano fourfolds
    Thibaut Delcroix

48. K-stability of P^3 blown up along the disjoint union of a twisted cubic curve and a line
    Elena Denisova

49. Stability of fibrations
    Ruadhai Dervan

50. Wall crossing for K-moduli spaces of plane curves
    Kristin DeVleming

51. The bottleneck degree of algebraic varieties
    Sandra Di Rocco

52. Dynamical filtrations|
    Tien-Cuong Dinh, Hsueh-Yung Lin, Keiji Oguiso and De-Qi Zhang

53. Roth's theorem for adelic curves
    Paolo Dolce and Francesco Zucconi

54. Enumerative geometry, fredholm analysis and moduli spaces of surfaces of general type Simon Donaldson

55. Bounding the complexity of 2-loop Feynman integrals
    Charles Doran

56. K-stability of P^3 blown up along smooth curves of genus 4 and degree 6
    Tiago Duarte Guerreiro

57. Rigidity of affine Brieskorn-Pham threefolds
    Adrien Dubouloz

58. Birational geometry and cylindricity of Severi-Brauer varieties
    Adrien Dubouloz, Kento Fujita, Takashi Kishimoto and Takuzo Okada

59. Okawa's theorem and wide subcategories of coherent sheaves on curves
    Alexey Elagin

60. Mixed Hodge structure decomposition of alexander modules into generalized eigenspaces
    Eva Elduque

61. Local stability threshold of Del Pezzo surfaces of degree 2
    Erroxe Etxabarri Alberdi

62. Rational simple connectedness and the quintic Del Pezzo threefold
    Andrea Fanelli

63. K3 structures from singular Fano varieties
    Enrico Fatighenti

64. An overview of homotopy path algebras
    David Favero

65. Quasi-invariants and free arrangements
    Misha Feigin

66. The Brasselet-Schurmann-Yokura conjecture on L-classes of singular varieties
    Javier Fernandez de Bobadilla and Irma Pallares Torres

67. Notes on motivic integration on Berkovich spaces
    Tommaso de Fernex

68. Counting sheaves by counting curves
    Soheyla Feyzbakhsh and Richard Thomas

69. On the boundedness of elliptically fibered Calabi-Yau threefolds
    Stefano Filipazzi

70. Connected algebraic groups acting on Fano fibrations over P^1
    Enrica Floris

71. Maximal automorphism groups of surfaces
    Pascal Fong and Matilde Maccan

72. A canonical Hodge theoretic projective structure on compact Riemann surfaces
    Paola Frediani

73. On extremal contractions of log canonical pairs
    Osamu Fujino

74. On the singular loci of higher secant varieties of Veronese embeddings
    Katsuhisa Furukawa

75. The…