A bidirectional many-to-one association is the most common kind of association. (This is the standard parent/child relationship.)

<class name="Person">
    <id name="id" column="personId">
        <generator class="native"/>
    </id>
    <many-to-one name="address" 
        column="addressId"
        not-null="true"/>
</class>

<class name="Address">
    <id name="id" column="addressId">
        <generator class="native"/>
    </id>
    <set name="people" inverse="true">
        <key column="addressId"/>
        <one-to-many class="Person"/>
    </set>
</class>

create table Person ( personId bigint not null primary key, addressId bigint not null )
create table Address ( addressId bigint not null primary key )
        

If you use a List (or other indexed collection) you need to set the key column of the foreign key to not null, and let Hibernate manage the association from the collections side to maintain the index of each element (making the other side virtually inverse by setting update="false" and insert="false"):

<class name="Person">
   <id name="id"/>
   ...
   <many-to-one name="address"
      column="addressId"
      not-null="true"
      insert="false"
      update="false"/>
</class>

<class name="Address">
   <id name="id"/>
   ...
   <list name="people">
      <key column="addressId" not-null="true"/>
      <list-index column="peopleIdx"/>
      <one-to-many class="Person"/>
   </list>
</class>

It is important that you define not-null="true" on the <key> element of the collection mapping if the underlying foreign key column is NOT NULL. Don't only declare not-null="true" on a possible nested <column> element, but on the <key> element.

A bidirectional one-to-one association on a foreign key is quite common.

<class name="Person">
    <id name="id" column="personId">
        <generator class="native"/>
    </id>
    <many-to-one name="address" 
        column="addressId" 
        unique="true"
        not-null="true"/>
</class>

<class name="Address">
    <id name="id" column="addressId">
        <generator class="native"/>
    </id>
   <one-to-one name="person" 
        property-ref="address"/>
</class>

create table Person ( personId bigint not null primary key, addressId bigint not null unique )
create table Address ( addressId bigint not null primary key )
        

A bidirectional one-to-one association on a primary key uses the special id generator.

<class name="Person">
    <id name="id" column="personId">
        <generator class="native"/>
    </id>
    <one-to-one name="address"/>
</class>

<class name="Address">
    <id name="id" column="personId">
        <generator class="foreign">
            <param name="property">person</param>
        </generator>
    </id>
    <one-to-one name="person" 
        constrained="true"/>
</class>

create table Person ( personId bigint not null primary key )
create table Address ( personId bigint not null primary key )