Nội dung được dịch bởi AI, chỉ mang tính chất tham khảo
Tiền lượng loại lớn cho các số giao điểm và thể tích của các lớp chính của vi phân bậc hai
Tóm tắt
Trong bài báo này, chúng tôi phân tích các tiệm cận loại lớn cho các số giao điểm giữa các lớp $$\psi $$, còn được gọi là các tương quan, trên không gian moduli của các đường cong ổn định. Chứng minh của chúng tôi được thực hiện thông qua phân tích tổ hợp các quan hệ đệ quy (các ràng buộc Virasoro) mà duy nhất xác định các tương quan này, cùng với việc so sánh giữa các hệ số trong các quan hệ này với xác suất nhảy của một kiểu đi ngẫu nhiên đơn giản bất đối xứng. Như một ứng dụng của kết quả này, chúng tôi cung cấp các giới hạn loại lớn cho các thể tích Masur–Veech và các hằng số Siegel–Veech liên quan đến các lớp chính trong không gian moduli của các vi phân bậc hai. Những kết quả này xác nhận các dự đoán của Delecroix–Goujard–Zograf–Zorich từ năm 2019.
Từ khóa
#tiệm cận loại lớn #số giao điểm #lớp chính #thể tích Masur–Veech #hằng số Siegel–Veech #vi phân bậc hai #không gian moduli #ràng buộc VirasoroTài liệu tham khảo
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