Mukai flops and Pl\"ucker type formulas for hyper-K\"ahler manifolds

TL;DR

This paper investigates the intersection theory of complex Lagrangian subvarieties in holomorphic symplectic manifolds, focusing on their behavior under Mukai flops and deriving a Plücker type formula for Legendre duals, with applications to projective dual varieties.

Contribution

It provides a rigorous proof of the Plücker type formula for Legendre dual subvarieties and explores their behavior under Mukai flops in hyper-Kähler manifolds.

Findings

Proof of the Plücker type formula for Legendre duals

Analysis of Lagrangian subvarieties under Mukai flops

Applications to projective dual varieties

Abstract

We study the intersection theory of complex Lagrangian subvarieties inside holomorphic symplectic manifolds. In particular, we study their behaviour under Mukai flops and give a rigorous proof of the Pl\"ucker type formula for Legendre dual subvarieties written down by the second author before. Then we apply the formula to study projective dual varieties in projective spaces.